Algebraic & Geometric Topology

Non-L–space integral homology $3$–spheres with no nice orderings

Xinghua Gao

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Abstract

We give infinitely many examples of non-L–space irreducible integer homology 3–spheres whose fundamental groups do not have nontrivial PSL˜2() representations.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2511-2522.

Dates
Received: 5 October 2016
Revised: 7 January 2017
Accepted: 20 January 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841450

Digital Object Identifier
doi:10.2140/agt.2017.17.2511

Mathematical Reviews number (MathSciNet)
MR3686404

Zentralblatt MATH identifier
1373.57036

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
L–space left orderability homology sphere $\mathrm{SL}_2(\mathbb{R})$ representation

Citation

Gao, Xinghua. Non-L–space integral homology $3$–spheres with no nice orderings. Algebr. Geom. Topol. 17 (2017), no. 4, 2511--2522. doi:10.2140/agt.2017.17.2511. https://projecteuclid.org/euclid.agt/1510841450


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References

  • J Bowden, Approximating $C^0$–foliations by contact structures, Geom. Funct. Anal. 26 (2016) 1255–1296
  • S Boyer, C,M Gordon, L Watson, On L-spaces and left-orderable fundamental groups, Math. Ann. 356 (2013) 1213–1245
  • P,J Callahan, M,V Hildebrand, J,R Weeks, A census of cusped hyperbolic $3$–manifolds, Math. Comp. 68 (1999) 321–332
  • D Cooper, M Culler, H Gillet, D,D Long, P,B Shalen, Plane curves associated to character varieties of $3$–manifolds, Invent. Math. 118 (1994) 47–84
  • M Culler, N,M Dunfield, Orderability and Dehn filling, preprint (2016)
  • M Culler, N,M Dunfield, M Goerner, J,R Weeks, SnapPy, a computer program for studying the geometry and topology of $3$–manifolds Available at \setbox0\makeatletter\@url http://snappy.computop.org {\unhbox0
  • M Culler, P,B Shalen, Varieties of group representations and splittings of $3$–manifolds, Ann. of Math. 117 (1983) 109–146
  • N,M Dunfield, Examples of non-trivial roots of unity at ideal points of hyperbolic $3$–manifolds, Topology 38 (1999) 457–465
  • X Gao, Non L–space integral homology $3$–spheres with no nice orderings, preprint (2016)
  • E Ghys, Groups acting on the circle, Enseign. Math. 47 (2001) 329–407
  • T,J Gillespie, L–space fillings and generalized solid tori, preprint (2016)
  • L,C Jeffrey, J Weitsman, Bohr–Sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula, Comm. Math. Phys. 150 (1992) 593–630
  • W,H Kazez, R Roberts, Approximating $C^{1,0}$–foliations, from “Interactions between low-dimensional topology and mapping class groups” (R,I Baykur, J Etnyre, U Hamenstädt, editors), Geom. Topol. Monogr. 19, Geom. Topol. Publ. (2015) 21–72
  • R Kirby, Problems in low-dimensional topology, preprint (1995) Available at \setbox0\makeatletter\@url https://math.berkeley.edu/~kirby/ {\unhbox0
  • P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311–334
  • P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281–1300
  • J Rasmussen, S,D Rasmussen, Floer simple manifolds and L–space intervals, preprint (2015)
  • W,A Stein, et al, Sage mathematics software (Version 6.10), The Sage Development Team (2015) Available at \setbox0\makeatletter\@url http://www.sagemath.org {\unhbox0
  • S Tillmann, Varieties associated to $3$–manifolds: finding hyperbolic structures of and surfaces in $3$–manifolds, lecture notes (2003) Available at \setbox0\makeatletter\@url http://www.maths.usyd.edu.au/u/tillmann/research.html {\unhbox0
  • R Zentner, Integer homology $3$–spheres admit irreducible representations in $\mathrm{SL}(2,\C)$, preprint (2016)