Osaka Journal of Mathematics Articles (Project Euclid)
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The latest articles from Osaka Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 22 Mar 2011 10:05 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Quotients of bounded homogeneous domains by cyclic groups
http://projecteuclid.org/euclid.ojm/1277298908
<strong>Christian Miebach</strong><p><strong>Source: </strong>Osaka J. Math., Volume 47, Number 2, 331--352.</p><p><strong>Abstract:</strong><br/>
Let $D$ be a bounded homogeneous domain in $\mathbb{C}^{n}$
and let $\varphi$ be an automorphism of $D$ which generates
a discrete subgroup $\Gamma$ of $\Aut_{\mathcal{O}}(D)$. It
is shown that the complex space $D/\Gamma$ is Stein.
</p>projecteuclid.org/euclid.ojm/1277298908_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTType numbers of quaternion hermitian forms and supersingular abelian varietieshttps://projecteuclid.org/euclid.ojm/1524038733<strong>Tomoyoshi Ibukiyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 369--384.</p><p><strong>Abstract:</strong><br/>
The word \textit{type number} of an algebra means classically the number of isomorphism classes of maximal orders in the algebra, but here we consider quaternion hermitian lattices in a fixed genus and their right orders. Instead of inner isomorphism classes of right orders, we consider isomorphism classes realized by similitudes of the quaternion hermitian forms.The number $T$ of such isomorphism classes are called \textit{type number} or \textit{$G$-type number}, where $G$ is the group of quaternion hermitian similitudes. We express $T$ in terms of traces of some special Hecke operators. This is a generalization of the result announced in [5] (I) from the principal genus to general lattices. We also apply our result to the number of isomorphism classes of any polarized superspecial abelian varieties which have a model over ${\Bbb F}_p$ such that the polarizations are in a "fixed genus of lattices". This is a generalization of [8] and has an application to the number of components in the supersingular locus which are defined over ${\Bbb F}_p$.
</p>projecteuclid.org/euclid.ojm/1524038733_20180418040536Wed, 18 Apr 2018 04:05 EDTA remark on conditions that a diffusion in the natural scale is a martingalehttps://projecteuclid.org/euclid.ojm/1524038734<strong>Yuuki Shimizu</strong>, <strong>Fumihiko Nakano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 385--391.</p><p><strong>Abstract:</strong><br/>
We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.
</p>projecteuclid.org/euclid.ojm/1524038734_20180418040536Wed, 18 Apr 2018 04:05 EDTOn the flat geometry of the cuspidal edgehttps://projecteuclid.org/euclid.ojm/1530691235<strong>Raúl Oset Sinha</strong>, <strong>Farid Tari</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 393--421.</p><p><strong>Abstract:</strong><br/>
We study the geometry of the cuspidal edge $M$ in $\mathbb{R}^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the contact of $M$ with planes from that classification. The contact of $M$ with lines is measured by the singularities of orthogonal projections of $M$. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in $S^2$. We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge.
</p>projecteuclid.org/euclid.ojm/1530691235_20180704040042Wed, 04 Jul 2018 04:00 EDTBloch's conjecture for Enriques varietieshttps://projecteuclid.org/euclid.ojm/1530691236<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 423--438.</p><p><strong>Abstract:</strong><br/>
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.
</p>projecteuclid.org/euclid.ojm/1530691236_20180704040042Wed, 04 Jul 2018 04:00 EDTRank-one Perturbation of Weighted Shifts on a Directed Tree: Partial Normality and Weak Hyponormalityhttps://projecteuclid.org/euclid.ojm/1530691237<strong>George R. Exner</strong>, <strong>Il Bong Jung</strong>, <strong>Eun Young Lee</strong>, <strong>Minjung Seo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 439--462.</p><p><strong>Abstract:</strong><br/>
A special rank-one perturbation $S_{t,n}$ of a weighted shift on a directed tree is constructed. Partial normality and weak hyponormality (including quasinormality, $p$-hyponormality, $p$-paranormality, absolute-$p$-paranormality and $A(p)$-class) of $S_{t,n}$ are characterized.
</p>projecteuclid.org/euclid.ojm/1530691237_20180704040042Wed, 04 Jul 2018 04:00 EDTOn-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Formshttps://projecteuclid.org/euclid.ojm/1530691238<strong>Shuwen Lou</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 463--477.</p><p><strong>Abstract:</strong><br/>
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not necessarily satisfy volume-doubling property. Assuming Nash-type inequality, it is proved in this paper that outside a properly exceptional set, if a pointwise on-diagonal heat kernel upper bound in terms of the volume function is known a priori, then the comparable heat kernel lower bound also holds. The only assumption made on the volume growth rate is that it can be bounded by a continuous function satisfying doubling property, in other words, is not exponential.
</p>projecteuclid.org/euclid.ojm/1530691238_20180704040042Wed, 04 Jul 2018 04:00 EDTMazur manifolds and corks with small shadow complexitieshttps://projecteuclid.org/euclid.ojm/1530691239<strong>Hironobu Naoe</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 479--498.</p><p><strong>Abstract:</strong><br/>
In this paper we show that there exist infinitely many Mazur type manifolds and corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow. We also find such manifolds among 4-manifolds constructed from Bing's house. Our manifolds with shadow complexity one contain the Mazur manifolds $W^{\pm }(l,k)$ which were studied by Akbulut and Kirby.
</p>projecteuclid.org/euclid.ojm/1530691239_20180704040042Wed, 04 Jul 2018 04:00 EDTOn Kohnen plus-space of Jacobi forms of half integral weight of matrix indexhttps://projecteuclid.org/euclid.ojm/1530691240<strong>Shuichi Hayashida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 499--522.</p><p><strong>Abstract:</strong><br/>
We introduce a plus-space of Jacobi forms, which is a certain subspace of Jacobi forms of half-integral weight of matrix index. This is an analogue to the Kohnen plus-space in the framework of Jacobi forms. We shall show a linear isomorphism between the plus-space of Jacobi forms and the space of Jacobi forms of integral weight of certain matrix index. Moreover, we shall show that this linear isomorphism is compatible with the action of Hecke operators of both spaces. This result is a kind of generalization of Eichler-Zagier-Ibukiyama correspondence, which is an isomorphism between the generalized plus-space of Siegel modular forms of general degree and Jacobi forms of index $1$ of general degree.
</p>projecteuclid.org/euclid.ojm/1530691240_20180704040042Wed, 04 Jul 2018 04:00 EDTAnswer to a Question by Nakamura, Nakanishi, and Satoh involving crossing numbers of knotshttps://projecteuclid.org/euclid.ojm/1530691241<strong>Jun Ge</strong>, <strong>Xian'an Jin</strong>, <strong>Louis H. Kauffman</strong>, <strong>Pedro Lopes</strong>, <strong>Lianzhu Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 523--527.</p><p><strong>Abstract:</strong><br/>
In this paper we give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh concerning an inequality involving crossing numbers of knots. We show it is an equality only for the trefoil and for the figure-eight knots.
</p>projecteuclid.org/euclid.ojm/1530691241_20180704040042Wed, 04 Jul 2018 04:00 EDT$L^2$-Burau maps and $L^2$-Alexander torsionshttps://projecteuclid.org/euclid.ojm/1530691242<strong>Fathi Ben Aribi</strong>, <strong>Anthony Conway</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 529--545.</p><p><strong>Abstract:</strong><br/>
It is well known that the Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define $L^2$-Burau maps and use them to compute some $L^2$-Alexander torsions of links. As an application, we prove that the $L^2$-Burau maps distinguish more braids than the Burau representation.
</p>projecteuclid.org/euclid.ojm/1530691242_20180704040042Wed, 04 Jul 2018 04:00 EDTInitial-boundary value problem for the degenerate hyperbolic equation of a hanging stringhttps://projecteuclid.org/euclid.ojm/1530691243<strong>Masahiro Takayama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 547--565.</p><p><strong>Abstract:</strong><br/>
We consider an initial-boundary value problem for the degenerate linear hyperbolic equation as a model of the motion of an inextensible string fixed at one end in the gravity field. We shall show the existence and the uniqueness of the solution and study the regularity of the solution.
</p>projecteuclid.org/euclid.ojm/1530691243_20180704040042Wed, 04 Jul 2018 04:00 EDTA complete description of the antipodal set of most symmetric spaces of compact typehttps://projecteuclid.org/euclid.ojm/1530691244<strong>Jonas Beyrer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 567--586.</p><p><strong>Abstract:</strong><br/>
It is known that the antipodal set of a Riemannian symmetric space of compact type $G/K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system $\mathfrak{a}_r$ and a non-trivial fundamental group, which is not isomorphic to $\mathbb{Z}_2$ or $\mathbb{Z}_{r+1}$. For example, we show that the antipodal sets of the Lie groups $Spin(2r+1)\:\: r\geq 5$, $E_8$ and $G_2$ consist only of one orbit which is of dimension $2r$, 128 and 6, respectively; $SO(2r+1)$ has also an antipodal set of dimension $2r$; and the Grassmannian $Gr_{r,r+q}(\mathbb{R})$ has a $rq$-dimensional orbit as antipodal set if $r\geq 5$ and $r\neq q>0$.
</p>projecteuclid.org/euclid.ojm/1530691244_20180704040042Wed, 04 Jul 2018 04:00 EDTOn the moment-angle manifold constructed by Fan, Chen, Ma and Wanghttps://projecteuclid.org/euclid.ojm/1539158659<strong>Kouyemon Iriye</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 587--593.</p><p><strong>Abstract:</strong><br/>
Fan, Chen, Ma and Wang [5] constructed a moment-angle manifold whose cohomology ring is isomorphic to that of the connected sum of sphere products consisting of one product of three spheres. In this paper, we show that these are in fact diffeomorphic.
</p>projecteuclid.org/euclid.ojm/1539158659_20181010040459Wed, 10 Oct 2018 04:04 EDTOn spectral measures of random Jacobi matriceshttps://projecteuclid.org/euclid.ojm/1539158661<strong>Trinh Khanh Duy</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 595--617.</p><p><strong>Abstract:</strong><br/>
The paper studies the limiting behaviour of spectral measures of random Jacobi matrices of Gaussian, Wishart and MANOVA beta ensembles. We show that the spectral measures converge weakly to a limit distribution which is the semicircle distribution, Marchenko-Pastur distributions or Kesten-McKay distributions, respectively. The Gaussian fluctuation around the limit is then investigated.
</p>projecteuclid.org/euclid.ojm/1539158661_20181010040459Wed, 10 Oct 2018 04:04 EDTA Danilov-type formula for toric origami manifolds via localization of indexhttps://projecteuclid.org/euclid.ojm/1539158664<strong>Hajime Fujita</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 619--645.</p><p><strong>Abstract:</strong><br/>
We give a direct geometric proof of a Danilov-type formula for toric origami manifolds by using the localization of Riemann-Roch number.
</p>projecteuclid.org/euclid.ojm/1539158664_20181010040459Wed, 10 Oct 2018 04:04 EDTAnalysis of Contact Cauchy--Riemann maps I: a priori $C^k$ estimates and asymptotic convergencehttps://projecteuclid.org/euclid.ojm/1539158665<strong>Yong-Geun Oh</strong>, <strong>Rui Wang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 647--679.</p><p><strong>Abstract:</strong><br/>
In the present article, we develop tensorial analysis for solutions $w$ of the following nonlinear elliptic system $$ {\overline \partial}^\pi w = 0, \, d(w^*\lambda \circ j) = 0, $$ associated to a contact triad $(M,\lambda,J)$. The novel aspect of this approach is that we work directly with this elliptic system on the contact manifold without involving the symplectization process. In particular, when restricted to the case where the one-form $w^*\lambda \circ j$ is exact, all a priori estimates for $w$-component can be written in terms of the map $w$ itself without involving the coordinate from the symplectization. We establish a priori $C^k$ coercive pointwise estimates for all $k \geq 2$ in terms of the energy density $\|dw\|^2$ by means of tensorial calculations on the contact manifold itself. Further, for any solution $w$ under the finite $\pi$-energy assumption and the derivative bound, we also establish the asymptotic subsequence convergence to `spiraling' instantons along the `rotating' Reeb orbit.
</p>projecteuclid.org/euclid.ojm/1539158665_20181010040459Wed, 10 Oct 2018 04:04 EDTInfinite algebraic subgroups of the real Cremona grouphttps://projecteuclid.org/euclid.ojm/1539158666<strong>Maria Fernanda Robayo</strong>, <strong>Susanna Zimmermann</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 681--712.</p><p><strong>Abstract:</strong><br/>
We give the classification of the maximal infinite algebraic subgroups of the real Cremona group of the plane up to conjugacy and present a parametrisation space of each conjugacy class. Moreover, we show that the real plane Cremona group is not generated by a countable union of its infinite algebraic subgroups.
</p>projecteuclid.org/euclid.ojm/1539158666_20181010040459Wed, 10 Oct 2018 04:04 EDTBergman iteration and $C^{\infty}$-convergence towards Kähler-Ricci flowhttps://projecteuclid.org/euclid.ojm/1539158667<strong>Ryosuke Takahashi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 713--729.</p><p><strong>Abstract:</strong><br/>
On a polarized manifold $(X,L)$, the Bergman iteration $\phi_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the Kähler-Ricci flow $\phi_t$ at any time $t \geq 0$ and the limiting behavior of metrics $\phi_k^{(m)}$ when $m=m(k)$ and the ratio $m/k$ approaches to $t$ as $k \to \infty$. Mainly, three settings are investigated: the case when $L$ is a general polarization on a Calabi-Yau manifold $X$ and the case when $L=\pm K_X$ is the (anti-) canonical bundle. Recently, Berman showed that the convergence $\phi_k^{(m)} \to \phi_t$ holds in the $C^0$-topology, in particular, the convergence of curvatures holds in terms of currents. In this paper, we extend Berman's result and show that this convergence actually holds in the smooth topology.
</p>projecteuclid.org/euclid.ojm/1539158667_20181010040459Wed, 10 Oct 2018 04:04 EDTCosmetic banding on knots and linkshttps://projecteuclid.org/euclid.ojm/1539158668<strong>Kazuhiro Ichihara</strong>, <strong>In Dae Jong</strong>, <strong>Hidetoshi Masai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 731--745.</p><p><strong>Abstract:</strong><br/>
We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic manifolds. This gives a counterexample to a conjecture raised by Bleiler, Hodgson and Weeks.
</p>projecteuclid.org/euclid.ojm/1539158668_20181010040459Wed, 10 Oct 2018 04:04 EDTToric weak Fano varieties associated to building setshttps://projecteuclid.org/euclid.ojm/1539158669<strong>Yusuke Suyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 747--760.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a building set to be weak Fano in terms of the building set.
</p>projecteuclid.org/euclid.ojm/1539158669_20181010040459Wed, 10 Oct 2018 04:04 EDTSelf-intersections of curves on a surface and Bernoulli numbershttps://projecteuclid.org/euclid.ojm/1539158670<strong>Shinji Fukuhara</strong>, <strong>Nariya Kawazumi</strong>, <strong>Yusuke Kuno</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 761--768.</p><p><strong>Abstract:</strong><br/>
We study an operation which measures self-intersections of curves on an oriented surface. It turns out that a certain computation on this topological operation is related to the Bernoulli numbers $B_m$, and our study yields a family of explicit formulas for $B_m$. As a special case, this family contains the celebrated formula for $B_m$ due to Kronecker.
</p>projecteuclid.org/euclid.ojm/1539158670_20181010040459Wed, 10 Oct 2018 04:04 EDTThe vertices of the components of the permutation module induced from parabolic groupshttps://projecteuclid.org/euclid.ojm/1539158671<strong>Lars Pforte</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 769--775.</p><p><strong>Abstract:</strong><br/>
We consider the permutation module $k_P{\uparrow^{{\rm GL}_n(p^f)}}$, where $P$ is a parabolic group in the general linear group ${\rm GL}_n(p^f)$ and $k$ is an algebraically closed field of prime characteristic $p$. The vertices of the components of these modules have been calculated in [9] by Tinberg, who studied these modules for all groups with split BN-pairs in characteristic $p$. In this paper we show that the idea of suitability is strong enough to find all $p$-groups that are vertex of some component of $k_P{\uparrow^{{\rm GL}_n(p^f)}}$. Furthermore using a result of Burry and Carlson we show that all components have a different vertex.
</p>projecteuclid.org/euclid.ojm/1539158671_20181010040459Wed, 10 Oct 2018 04:04 EDTZero noise limit of a stochastic differential equation involving a local timehttps://projecteuclid.org/euclid.ojm/1539158672<strong>Kazumasa Kuwada</strong>, <strong>Taro Matsumura</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 777--794.</p><p><strong>Abstract:</strong><br/>
This paper studies the zero noise limit for the solution of a class of one-dimensional stochastic differential equations involving local time with irregular drift. These solutions are expected to approach one of the solutions to the ordinary differential equation formally obtained by cutting off the noise term. By determining the limit, we reveal that the presence of the local time really affects the asymptotic behavior, while it is observed only when intensity of the drift term is close to symmetric around the irregular point. Related with this problem, we also establish the Wentzel-Freidlin type large deviation principle.
</p>projecteuclid.org/euclid.ojm/1539158672_20181010040459Wed, 10 Oct 2018 04:04 EDTon the complexity of finite subgraphs of the curve graphhttps://projecteuclid.org/euclid.ojm/1539158673<strong>Edgar A. Bering IV</strong>, <strong>Gabriel Conant</strong>, <strong>Jonah Gaster</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 4, 795--808.</p><p><strong>Abstract:</strong><br/>
We say a graph has property $\mathcal{P}_{g,p}$ when it is an induced subgraph of the curve graph of a surface of genus $g$ with $p$ punctures. Two well-known graph invariants, the chromatic and clique numbers, can provide obstructions to $\mathcal{P}_{g,p}$. We introduce a new invariant of a graph, the \emph{nested complexity length}, which provides a novel obstruction to $\mathcal{P}_{g,p}$. For the curve graph this invariant captures the topological complexity of the surface in graph-theoretic terms; indeed we show that its value is $6g-6+2p$, i.e. twice the size of a maximal multicurve on the surface. As a consequence we show that large `half-graphs' do not have $\mathcal{P}_{g,p}$, and we deduce quantitatively that almost all finite graphs which pass the chromatic and clique tests do not have $\mathcal{P}_{g,p}$. We also reinterpret our obstruction in terms of the first-order theory of the curve graph, and in terms of RAAG subgroups of the mapping class group (following Kim and Koberda). Finally, we show that large complete multipartite graphs cannot have $\mathcal{P}_{g,p}$. This allows us to compute the upper density of the curve graph, and to conclude that clique size, chromatic number, and nested complexity length are not sufficient to determine $\mathcal{P}_{g,p}$.
</p>projecteuclid.org/euclid.ojm/1539158673_20181010040459Wed, 10 Oct 2018 04:04 EDTNon-flat totally geodesic surfaces in symmetric spaces of classical typehttps://projecteuclid.org/euclid.ojm/1547607623<strong>Katsuya Mashimo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 1--32.</p><p><strong>Abstract:</strong><br/>
We give a classification of non-flat totally geodesic surfaces in compact Riemannian symmetric spaces of classical type.
</p>projecteuclid.org/euclid.ojm/1547607623_20190115220101Tue, 15 Jan 2019 22:01 ESTOn Hochster's formula for a class of quotient spaces of moment-angle complexeshttps://projecteuclid.org/euclid.ojm/1547607624<strong>Li Yu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 33--50.</p><p><strong>Abstract:</strong><br/>
Any finite simplicial complex $\mathcal{K}$ and a partition of the vertex set of $\mathcal{K}$ determines a canonical quotient space of the moment-angle complex of ${\mathcal K}$. We prove that the cohomology groups of such a space can be computed via some Hochster's type formula, which generalizes the usual Hochster's formula for the cohomology groups of moment-angle complexes. In addition, we show that the stable decomposition of moment-angle complexes can also be extended to such spaces. This type of spaces include all the quasitoric manifolds that are pullback from the linear models. And we prove that the moment-angle complex associated to a finite simplicial poset is always homotopy equivalent to one of such spaces.
</p>projecteuclid.org/euclid.ojm/1547607624_20190115220101Tue, 15 Jan 2019 22:01 ESTThe virtual Thurston seminorm of 3-manifoldshttps://projecteuclid.org/euclid.ojm/1547607625<strong>Michel Boileau</strong>, <strong>Stefan Friedl</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 51--63.</p><p><strong>Abstract:</strong><br/>
We show that the Thurston seminorms of all finite covers of an aspherical 3-manifold determine whether it is a graph manifold, a mixed 3-manifold or hyperbolic.
</p>projecteuclid.org/euclid.ojm/1547607625_20190115220101Tue, 15 Jan 2019 22:01 ESTPositivity of anticanonical divisors from the viewpoint of Fano conic bundleshttps://projecteuclid.org/euclid.ojm/1547607626<strong>E. A. Romano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 65--74.</p><p><strong>Abstract:</strong><br/>
We give the first examples of flat fiber type contractions of Fano manifolds onto varieties that are not weak Fano, and we prove that these morphisms are Fano conic bundles. We also review some known results about the interaction between the positivity properties of anticanonical divisors of varieties of contractions.
</p>projecteuclid.org/euclid.ojm/1547607626_20190115220101Tue, 15 Jan 2019 22:01 ESTOn generalized Dold manifoldshttps://projecteuclid.org/euclid.ojm/1547607627<strong>Avijit Nath</strong>, <strong>Parameswaran Sankaran</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 75--90.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a smooth manifold with a (smooth) involution $\sigma:X\to X$ such that ${\rm Fix}(\sigma)\ne \emptyset$. We call the space $P(m,X):=\mathbb{S}^m\times X/\!\sim$ where $(v,x)\sim (-v,\sigma(x))$ a generalized Dold manifold. When $X$ is an almost complex manifold and the differential $T\sigma: TX\to TX$ is conjugate complex linear on each fibre, we obtain a formula for the Stiefel-Whitney polynomial of $P(m,X)$ when $H^1(X;\mathbb{Z}_2)=0$. We obtain results on stable parallelizability of $P(m,X)$ and a very general criterion for the (non) vanishing of the unoriented cobordism class $[P(m,X)]$ in terms of the corresponding properties for $X$. These results are applied to the case when $X$ is a complex flag manifold.
</p>projecteuclid.org/euclid.ojm/1547607627_20190115220101Tue, 15 Jan 2019 22:01 ESTAbelian subgroups of the mapping class groups for non-orientable surfaceshttps://projecteuclid.org/euclid.ojm/1547607628<strong>Erika Kuno</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 91--100.</p><p><strong>Abstract:</strong><br/>
One of the basic and important problems to study algebraic structures of the mapping class groups is finding abelian subgroups included in the mapping class groups. Birman-Lubotzky-McCarthy gave the answer of this question for the orientable surfaces, namely, they proved that any abelian subgroup of the mapping class groups for orientable surfaces of genus $g$ with $b$ boundary components and $c$ connected components is finitely generated and the maximal torsion-free rank of it is $3g+b-3c$. In the present paper, we prove that any abelian subgroup of the mapping class group of a compact connected non-orientable surface $N$ of genus $g\geq 1$ with $n\geq 0$ boundary components whose Euler characteristic is negative is finitely generated and the maximal torsion-free rank of it is $\frac{3}{2}(g-1)+n-2$ if $g$ is odd and $\frac{3}{2}g+n-3$ if $g$ is even.
</p>projecteuclid.org/euclid.ojm/1547607628_20190115220101Tue, 15 Jan 2019 22:01 ESTParametrization for a class of Rauzy Fractalshttps://projecteuclid.org/euclid.ojm/1547607629<strong>J. Bastos</strong>, <strong>T. Rodrigues de Souza</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 101--122.</p><p><strong>Abstract:</strong><br/>
In this paper, we study a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we give explicitly an automaton that generates the boundary of ${\mathcal R}_a$ and using an unusual numeration system we prove that ${\mathcal R}_a$ is homeomorphic to a topological disk.
</p>projecteuclid.org/euclid.ojm/1547607629_20190115220101Tue, 15 Jan 2019 22:01 ESTThe Socle of the Last Term in the Minimal Injective Resolution of a Gorenstein Modulehttps://projecteuclid.org/euclid.ojm/1547607630<strong>Weiling Song</strong>, <strong>Xiaojin Zhang</strong>, <strong>Zhaoyong Huang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 123--132.</p><p><strong>Abstract:</strong><br/>
Let $R$ be a left Noetherian ring, $S$ a right Noetherian ring and $_RU$ a Gorenstein module with $S={\rm End}(_RU)$. If the injective dimensions of $_RU$ and $U_S$ are finite, then the last term in the minimal injective resolution of $_{R}U$ has an essential socle.
</p>projecteuclid.org/euclid.ojm/1547607630_20190115220101Tue, 15 Jan 2019 22:01 ESTFoldings and two-sided tilting complexes for Brauer tree algebrashttps://projecteuclid.org/euclid.ojm/1547607631<strong>Yuta Kozakai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 133--164.</p><p><strong>Abstract:</strong><br/>
In this note, for a Brauer tree algebra $A$ and a star-shaped Brauer tree algebra $B$ which is derived equivalent to $A$, we give operations on the two-sided tilting complex $D_T$ of $A\otimes B^{op}$-modules constructed in [3] which is isomorphic to the Rickard tree-to-star complex $T$ constructed in [5] in $D^b(A)$, and we show that the operations on $D_T$ correspond to operations called $foldings$ on the Rickard tree-to-star complex $T$ given in [7].
</p>projecteuclid.org/euclid.ojm/1547607631_20190115220101Tue, 15 Jan 2019 22:01 ESTUnstabilized weakly reducible Heegaard splittingshttps://projecteuclid.org/euclid.ojm/1547607632<strong>Kun Du</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 165--172.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a sufficient condition for a (weakly reducible) Heegaard splitting to be unstabilized and uncritical. We also give a sufficient condition for a Heegaard splitting to be critical.
</p>projecteuclid.org/euclid.ojm/1547607632_20190115220101Tue, 15 Jan 2019 22:01 ESTPerfect fluid spacetimes with harmonic generalized curvature tensorhttps://projecteuclid.org/euclid.ojm/1547607633<strong>Carlo Alberto Mantica</strong>, <strong>Uday Chand De</strong>, <strong>Young Jin Suh</strong>, <strong>Luca Guido Molinari</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 173--182.</p><p><strong>Abstract:</strong><br/>
We show that $n$-dimensional perfect fluid spacetimes with diver\-gen\-ce-free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under certain conditions, GRW spacetimes. As particular cases, perfect fluids with divergence-free projective, concircular, conharmonic or quasi-conformal curvature tensor are GRW spacetimes. Finally, we explore some physical consequences of such results.
</p>projecteuclid.org/euclid.ojm/1547607633_20190115220101Tue, 15 Jan 2019 22:01 ESTFrobenius structures and characters of affine Lie algebrashttps://projecteuclid.org/euclid.ojm/1547607634<strong>Ikuo Satake</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 1, 183--212.</p><p><strong>Abstract:</strong><br/>
The explicit description of the Frobenius structure for the elliptic root system of type $D_4^{(1,1)}$ in terms of the characters of an affine Lie algebra of type $D_4^{(1)}$ is given.
</p>projecteuclid.org/euclid.ojm/1547607634_20190115220101Tue, 15 Jan 2019 22:01 ESTA classification problem on mapping classes on fiber spaces over Teichmüller spaceshttps://projecteuclid.org/euclid.ojm/1554278420<strong>Yingqing Xiao</strong>, <strong>Chaohui Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 213--227.</p><p><strong>Abstract:</strong><br/>
Let $\tilde{S}$ be an analytically finite Riemann surface which is equipped with a hyperbolic metric. Let $S=\tilde{S}\backslash \{\mbox{one point}\ x\}$. There exists a natural projection $\Pi$ of the $x$-pointed mapping class group Mod$_S^x$ onto the mapping class group Mod$(\tilde{S})$. In this paper, we classify elements in the fiber $\Pi^{-1}(\chi)$ for an elliptic element $\chi\in \mbox{Mod}(\tilde{S})$, and give a geometric interpretation for each element in $\Pi^{-1}(\chi)$. We also prove that $\Pi^{-1}(t_a^n\circ \chi)$ or $\Pi^{-1}(t_a^n\circ \chi^{-1})$ consists of hyperbolic mapping classes provided that $t_a^n\circ \chi$ and $t_a^n\circ \chi^{-1}$ are hyperbolic, where $a$ is a simple closed geodesic on $\tilde{S}$ and $t_a$ is the positive Dehn twist along $a$.
</p>projecteuclid.org/euclid.ojm/1554278420_20190403040038Wed, 03 Apr 2019 04:00 EDTA Block Refinement of the Green-Puig Parameterization of the Isomorphism Types of Indecomposable Moduleshttps://projecteuclid.org/euclid.ojm/1554278421<strong>Morton E. Harris</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 229--236.</p><p><strong>Abstract:</strong><br/>
Let $p$ be a prime integer, let $\mathcal{O}$ be a commutative complete local Noetherian ring with an algebraically closed residue field $k$ of charateristic $p$ and let$G$ be a finite group. Let $P$ be a $p$-subgroup of $G$ and let $X$ be an indecomposable $\mathcal{O} P$-module with vertex $P$. Let $\Lambda (G,P,X)$ denote a set of representatives for the isomorphism classes of indecomposable $\mathcal{O} G$-modules with vertex-source pair $(P,X)$ (so that $\Lambda(G,P,X)$ is a finite set by the Green correspondence). As mentioned in [5, Notes on Section~26], L. Puig asserted that a defect multiplicity module determined by $(P,X)$ can be used to obtain an extended parameterization of $\Lambda(G,P,X)$. In [5, Proposition 26.3], J. Thévenaz completed this program under the hypotheses that $X$ is $\mathcal{O}$-free. Here we use the methods of proof of [5, Theorem 26.3] to show that the $\mathcal{O}$-free hypothesis on $X$ is superfluous. (M. Linckelmann has also proved this, cf. [3]). Let $B$ be a block of $\mathcal{O} G$. Then we obtain a corresponding paramaterization of the $(\mathcal{O} G)B$-modules in $\Lambda(G,P,X)$.
</p>projecteuclid.org/euclid.ojm/1554278421_20190403040038Wed, 03 Apr 2019 04:00 EDTToric manifolds over cyclohedrahttps://projecteuclid.org/euclid.ojm/1554278422<strong>Seonjeong Park</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 237--254.</p><p><strong>Abstract:</strong><br/>
We study the action of the dihedral group on the (equivariant) cohomology of the toric manifolds associated with cycle graphs.
</p>projecteuclid.org/euclid.ojm/1554278422_20190403040038Wed, 03 Apr 2019 04:00 EDTA Markov's theorem for extended welded braids and linkshttps://projecteuclid.org/euclid.ojm/1554278423<strong>Celeste Damiani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 255--268.</p><p><strong>Abstract:</strong><br/>
Extended welded links are a generalization of Fenn, Rimányi, and Rourke's welded links. Their braided counterpart are extended welded braids, which are closely related to ribbon braids and loop braids. In this paper we prove versions of Alexander and Markov's theorems for extended welded braids and links, following Kamada's approach to the case of welded objects.
</p>projecteuclid.org/euclid.ojm/1554278423_20190403040038Wed, 03 Apr 2019 04:00 EDTUniform well-posedness for a time-dependent Ginzburg-Landau model in superconductivityhttps://projecteuclid.org/euclid.ojm/1554278424<strong>Jishan Fan</strong>, <strong>Bessem Samet</strong>, <strong>Yong Zhou</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 269--276.</p><p><strong>Abstract:</strong><br/>
We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient 0 < $\epsilon$ < 1 in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when $\epsilon=0$.
</p>projecteuclid.org/euclid.ojm/1554278424_20190403040038Wed, 03 Apr 2019 04:00 EDTCurves with maximally computed Clifford indexhttps://projecteuclid.org/euclid.ojm/1554278425<strong>Takao Kato</strong>, <strong>Gerriet Martens</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 277--288.</p><p><strong>Abstract:</strong><br/>
We say that a curve $X$ of genus $g$ has maximally computed Clifford index if the Clifford index $c$ of $X$ is, for $c>2$, computed by a linear series of the maximum possible degree $d$ < $g$; then $d = 2c+3$ resp. $d = 2c+4$ for odd resp. even $c$. For odd $c$ such curves have been studied in [6]. In this paper we analyze if/how far analoguous results hold for such curves of even Clifford index $c$.
</p>projecteuclid.org/euclid.ojm/1554278425_20190403040038Wed, 03 Apr 2019 04:00 EDTReduced contragredient Lie algebras and PC Lie algebrashttps://projecteuclid.org/euclid.ojm/1554278426<strong>Nagatoshi Sasano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 289--299.</p><p><strong>Abstract:</strong><br/>
Using the theory of standard pentads, we can embed an arbitrary finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation into some larger graded Lie algebra. However, it is not easy to find the structure of the ``larger graded Lie algebra'' from the definition in general cases. Under these, the first aim of this paper is to show that the ``larger graded Lie algebra'' is isomorphic to some PC Lie algebra, which are Lie algebras corresponding to special standard pentads called pentads of Cartan type. The second aim is to find the structure of a PC Lie algebra.
</p>projecteuclid.org/euclid.ojm/1554278426_20190403040038Wed, 03 Apr 2019 04:00 EDTCleft Coextension for symmetric twisted partial coactions on coalgebrashttps://projecteuclid.org/euclid.ojm/1554278427<strong>Q.-G. Chen</strong>, <strong>B. Yang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 301--322.</p><p><strong>Abstract:</strong><br/>
In this paper, we will introduce the concepts of symmetric twisted partial Hopf coactions, and discuss under which conditions a given symmetric twisted partial Hopf coaction is globalizable. Then we will introduce the notion of partial cleft coextensions which are dual to partial cleft extensions introduced by M. M. S. Alves et.al., and discuss its relation with partial crossed coproducts introduced by the first author of this paper, which covers the classical results in classical Hopf algebra theory.
</p>projecteuclid.org/euclid.ojm/1554278427_20190403040038Wed, 03 Apr 2019 04:00 EDTSTRONG-VISCOSITY SOLUTIONS: CLASSICAL AND PATH-DEPENDENT PDEshttps://projecteuclid.org/euclid.ojm/1554278428<strong>Andrea Cosso</strong>, <strong>Francesco Russo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 323--373.</p><p><strong>Abstract:</strong><br/>
The aim of the present work is the introduction of a viscosity type solution, called $strong$-$viscosity$ $solution$ emphasizing also a similarity with the existing notion of $strong$ $solution$ in the literature. It has the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.
</p>projecteuclid.org/euclid.ojm/1554278428_20190403040038Wed, 03 Apr 2019 04:00 EDTHopf bands in arborescent Hopf plumbingshttps://projecteuclid.org/euclid.ojm/1554278429<strong>Filip Misev</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 375--389.</p><p><strong>Abstract:</strong><br/>
For a positive Hopf plumbed arborescent Seifert surface $S$, we study the set of Hopf bands $H\subset S$, up to homology and up to the action of the monodromy. The classification of Seifert surfaces for which this set is finite is closely related to the classification of finite Coxeter groups.
</p>projecteuclid.org/euclid.ojm/1554278429_20190403040038Wed, 03 Apr 2019 04:00 EDTInvariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operatorshttps://projecteuclid.org/euclid.ojm/1554278430<strong>Roberto A. Prado</strong>, <strong>Ruy C. Charão</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 391--416.</p><p><strong>Abstract:</strong><br/>
We establish invariants for the trace map associated to a family of 1D discrete Dirac operators with Sturmian potentials. Using these invariants we prove that the operators have purely singular continuous spectrum of zero Lebesgue measure, uniformly on the mass and parameters that define the potentials. For rotation numbers of bounded density we prove that these Dirac operators have purely $\alpha$-continuous spectrum, as to the Schrödinger case, for some $\alpha \in (0,1)$. To the Sturmian Schrödinger and Dirac models we establish a comparison between invariants of the trace maps, which allows to compare the numbers $\alpha$'s and lower bounds on transport exponents.
</p>projecteuclid.org/euclid.ojm/1554278430_20190403040038Wed, 03 Apr 2019 04:00 EDTHomotopy groups of certain highly connected manifolds via loop space homologyhttps://projecteuclid.org/euclid.ojm/1554278431<strong>Samik Basu</strong>, <strong>Somnath Basu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 2, 417--430.</p><p><strong>Abstract:</strong><br/>
For $n\geq 2$ we consider $(n-1)$-connected closed manifolds of dimension at most $(3n-2)$. We prove that away from a finite set of primes, the $p$-local homotopy groups of $M$ are determined by the dimension of the space of indecomposable elements in the cohomology ring $H^\ast(M; \mathbb{Q})$. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. This generalizes some of the results of our earlier work [1].
</p>projecteuclid.org/euclid.ojm/1554278431_20190403040038Wed, 03 Apr 2019 04:00 EDTRemarks on Artin Approximation with constraintshttps://projecteuclid.org/euclid.ojm/1563242417<strong>Dorin Popescu</strong>, <strong>Guillaume Rond</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 431--440.</p><p><strong>Abstract:</strong><br/>
We study various approximation results of solutions of equations $f(x,Y)=0$ where $f(x,Y)\in\mathbb{K}[\![x]\!][Y]^r$ and $x$ and $Y$ are two sets of variables, and where some components of the solutions $y(x)\in\mathbb{K}[\![x]\!]^m$ do not depend on all the variables $x_j$. These problems were highlighted by M. Artin.
</p>projecteuclid.org/euclid.ojm/1563242417_20190715220050Mon, 15 Jul 2019 22:00 EDTResults on the topology of generalized real Bott manifoldshttps://projecteuclid.org/euclid.ojm/1563242418<strong>Raisa Dsouza</strong>, <strong>V. Uma</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 441--458.</p><p><strong>Abstract:</strong><br/>
Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh in [4]. In this article we extend the results of [7] on the topology of real Bott manifolds to generalized real Bott manifolds. We give a presentation of the fundamental group, prove that it is solvable and give a characterization for it to be abelian. We further prove that these manifolds are aspherical only in the case of real Bott manifolds and compute the higher homotopy groups. Furthermore, using the presentation of the cohomology ring with $\mathbb Z_2$-coefficients, we derive a combinatorial characterization for orientablity and spin structure.
</p>projecteuclid.org/euclid.ojm/1563242418_20190715220050Mon, 15 Jul 2019 22:00 EDTOn the non-periodic stable Auslander-Reiten Heller component for the Kronecker algebra over a complete discrete valuation ringhttps://projecteuclid.org/euclid.ojm/1563242420<strong>Kengo Miyamoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 459--496.</p><p><strong>Abstract:</strong><br/>
We consider the Kronecker algebra $A=\mathcal{O}[X,Y]/(X^2,Y^2)$, where $\mathcal{O}$ is a complete discrete valuation ring. Since $A\otimes\kappa$ is a special biserial algebra, where $\kappa$ is the residue field of $\mathcal{O}$, one can compute a complete list of indecomposable $A\otimes \kappa$-modules. For each indecomposable $A\otimes \kappa$-module, we obtain a special kind of $A$-lattices called ``Heller lattices''. In this paper, we determine the non-periodic component of a variant of the stable Auslander--Reiten quiver for the category of $A$-lattices that contains ``Heller lattices''.
</p>projecteuclid.org/euclid.ojm/1563242420_20190715220050Mon, 15 Jul 2019 22:00 EDTUntwisting number and Blanchfield pairingshttps://projecteuclid.org/euclid.ojm/1563242421<strong>Maciej Borodzik</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 497--505.</p><p><strong>Abstract:</strong><br/>
In this note we use Blanchfield forms to study knots that can be turned into an unknot using a single $\overline{t}_{2k}$ move.
</p>projecteuclid.org/euclid.ojm/1563242421_20190715220050Mon, 15 Jul 2019 22:00 EDTDirac operators on the Fefferman spin spaces in almost CR-geometryhttps://projecteuclid.org/euclid.ojm/1563242422<strong>Masayoshi Nagase</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 507--524.</p><p><strong>Abstract:</strong><br/>
A spin structure on a contact Riemannian manifold carries a spin structure on a circle bundle over the manifold. We have interest in the Dirac operators associated with those structures. In terms of a modified Tanno connection, relations between them are studied and some kinds of their explicit expressions are offered.
</p>projecteuclid.org/euclid.ojm/1563242422_20190715220050Mon, 15 Jul 2019 22:00 EDTVirtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairshttps://projecteuclid.org/euclid.ojm/1563242423<strong>Marco A. Farinati</strong>, <strong>Juliana García Galofre</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 525--547.</p><p><strong>Abstract:</strong><br/>
Given a set $X$, we provide the algebraic counterpart of the (mixed) Reidemeister moves for virtual knots and links, with semi-arcs labeled by $X$: we define (commutative and noncommutative) invariants with values in groups, using ``2-cocycles", and we also introduce a universal group $U_{nc}^{fg}(X)$ and functions $\pi_f, \pi_g\colon X\times X\to U_{nc}^{fg}(X)$ governing all 2-cocycles in $X$. We exhibit examples of computations -of the group and their invariants- achieved using GAP [7].
</p>projecteuclid.org/euclid.ojm/1563242423_20190715220050Mon, 15 Jul 2019 22:00 EDTToroidal surgeries and the genus of a knothttps://projecteuclid.org/euclid.ojm/1563242424<strong>Mario Eudave-muñoz</strong>, <strong>Araceli Guzmán-tristán</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 549--575.</p><p><strong>Abstract:</strong><br/>
In this paper we give an upper bound for the slopes yielding an incompressible torus by surgery on a hyperbolic knot in the 3-sphere in terms of its genus.
</p>projecteuclid.org/euclid.ojm/1563242424_20190715220050Mon, 15 Jul 2019 22:00 EDTOn a class of Rauzy fractals without the finiteness propertyhttps://projecteuclid.org/euclid.ojm/1563242425<strong>Gustavo A. Pavani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 577--599.</p><p><strong>Abstract:</strong><br/>
We present some topological and arithmetical aspects of a class of Rauzy fractals $\mathcal{R}_{a,b}$ related to the polynomials of the form $P_{a,b}(x)=x^{3}-ax^{2}-bx-1$, where $a$ and $b$ are integers satisfying $-a+1 \leq b \leq -2$. This class has the property that $0$ lies on the boundary of $\mathcal{R}_{a,b}$. We construct explicit finite automata that recognize the boundaries of these fractals. This allows to establish the number of neighbors of $\mathcal{R}_{a,b}$ in the tiling it generates. Furthermore, we prove that if $2a+3b+4 \leq 0$ then $\mathcal{R}_{a,b}$ is not homeomorphic to a topological disk. We also show that the boundary of the set $\mathcal{R}_{3,-2}$ is generated by two infinite iterated function systems.
</p>projecteuclid.org/euclid.ojm/1563242425_20190715220050Mon, 15 Jul 2019 22:00 EDTLagrangian submanifolds in strict nearly Kähler 6-manifoldshttps://projecteuclid.org/euclid.ojm/1563242426<strong>Hông Vân Lê</strong>, <strong>Lorenz Schwachhöfer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 601--629.</p><p><strong>Abstract:</strong><br/>
Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in $G_2$-manifolds. We prove that the mean curvature of a Lagrangian submanifold $L$ in a nearly Kähler manifold $(M, J, g)$ is symplectically dual to the Maslov 1-form on $L$. Using relative calibrations, we derive a formula for the second variation of the volume of a Lagrangian submanifold $L^3$ in a strict nearly Kähler manifold $(M^6, J, g)$ and compare it with McLean's formula for special Lagrangian submanifolds. We describe a finite dimensional local model of the moduli space of compact Lagrangian submanifolds in a strict nearly Kähler 6-manifold. We show that there is a real analytic atlas on $(M^6, J, g)$ in which the strict nearly Kähler structure $(J, g)$ is real analytic. Furthermore, w.r.t. an analytic strict nearly Kähler structure the moduli space of Lagrangian submanifolds of $M^6$ is a real analytic variety, whence infinitesimal Lagrangian deformations are smoothly obstructed if and only if they are formally obstructed. As an application, we relate our results to the description of Lagrangian submanifolds in the sphere $S^6$ with the standard nearly Kähler structure described in [34].
</p>projecteuclid.org/euclid.ojm/1563242426_20190715220050Mon, 15 Jul 2019 22:00 EDTRemarks on Föllmer's pathwise Itô calculushttps://projecteuclid.org/euclid.ojm/1563242427<strong>Yuki Hirai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 631--660.</p><p><strong>Abstract:</strong><br/>
We extend some results about Föllmer's pathwise Itô calculus that have only been derived for continuous paths to càdlàg paths with quadratic variation. We study some fundamental properties of pathwise Itô integrals with respect to càdlàg integrators, especially associativity and the integration by parts formula. Moreover, we study integral equations with respect to pathwise Itô integrals. We prove that some classes of integral equations, which can be explicitly solved in the usual stochastic calculus, can also be solved within the framework of Föllmer's calculus.
</p>projecteuclid.org/euclid.ojm/1563242427_20190715220050Mon, 15 Jul 2019 22:00 EDTRooted trees with the same plucking polynomialhttps://projecteuclid.org/euclid.ojm/1563242428<strong>Zhiyun Cheng</strong>, <strong>Sujoy Mukherjee</strong>, <strong>Józef H. Przytycki</strong>, <strong>Xiao Wang</strong>, <strong>Seung Yeop Yang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 56, Number 3, 661--674.</p><p><strong>Abstract:</strong><br/>
In this paper we address the following question: When do two rooted trees have the same plucking polynomial? The solution provided in the present paper has an algebraic version (Theorem 2.5) and a geometric version (Theorem 1.2). Furthermore, we give a criterion for a sequence of non-negative integers to be realized as a rooted tree.
</p>projecteuclid.org/euclid.ojm/1563242428_20190715220050Mon, 15 Jul 2019 22:00 EDT