Pacific Journal of Mathematics

The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold.

Ruth Charney and Michael Davis

Article information

Pacific J. Math., Volume 171, Number 1 (1995), 117-137.

First available in Project Euclid: 6 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57Q05: General topology of complexes


Charney, Ruth; Davis, Michael. The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. Pacific J. Math. 171 (1995), no. 1, 117--137.

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  • [B] W. Ballman, Singular spaces of non-positive curvature, Chapitre 10 in "Sur les Groupes Hyperboliques d'apres Mikhael Gromov," edited by E. Ghys and P. de la Harpe, Progress in Math. 81, Birkhauser, Boston, Basel, Berlin, 1990.
  • [Bo] N. Bourbaki, "Groupes et Algebres de Lie," Chapitres IV-VI, Hermann, Paris, 1968.
  • [Br] M.R. Bridson, Geodesies and curvature in metric simplicial complexes, in "Group Theory from a Geometrical Viewpoint," edited by E. Ghys, A. Haefliger, and A. Verjovsky, World Scientific, Singapore, 1991, 373-463.
  • [CD1] R. Charney and M.W. Davis, Singular metrics of nonpositive curvature on branched covers of Riemannianmanifolds, Amer. J. Math., 115 (1993), 929-1009.
  • [CD2] R. Charney and M.W. Davis, The polar dual of a convex polyhedral set in hyperbolic space, to appear in Michigan Math. J.
  • [C] J. Cheeger, Spectral geometry of singular Riemannianspaces, J. Differential Geom- etry, 18 (1983), 575-657.
  • [CMS] J. Cheeger, W. Miller, and R. Schrader, On the curvature of piecewise flat spaces, Commun. Math. Phys., 92 (1984), 405-454.
  • [Ch] S.S. Chern, On curvature and characteristic classes of a Riemannianmanifold, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 117-126.
  • [Dl] M.W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math., 117 (1983), 293-324.
  • [D2] M.W. Davis, Coxeter groups and aspherical manifolds, in "Algebraic Topology Aarhus 1982," edited by I. Madsen and B. Oliver, Springer Lee. Notes in Math., 1051, Springer-Verlag, New York and Berlin, 1984, 197-221.
  • [Ge] R. Geroch, Positive sectional curvature does not imply positive Gauss-Bonnet inte- grand, Proc. Amer. Math. Soc, 54 (1976), 267-270.
  • [G] M. Gromov, Hyperbolic groups, in "Essays in Group Theory," edited by S.M. Ger- sten, M.S.R.I. Publ. 8, Springer-Verlag, New York and Berlin, 1987, 75-264.
  • [M] G. Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University, 1988.
  • [SI] R. Stanley, Combinatorics and Commutative Algebra, Progress in Math., 41, Birkhauser, Boston, 1983.
  • [S2] R. Stanley, Flag f-vectorsand the cd-index, Math. Zeitschrift, 216 (1994), 483-499.
  • [W] D.W. Walkup, The lower bound conjecture for 3- and 4-manifolds, Acta Math., 125 (1970), 75-107.