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Random groups contain surface subgroups


Authors: Danny Calegari and Alden Walker
Journal: J. Amer. Math. Soc. 28 (2015), 383-419
MSC (2010): Primary 20P05, 20F65, 57M07; Secondary 57M20
DOI: https://doi.org/10.1090/S0894-0347-2014-00802-X
Published electronically: June 10, 2014
MathSciNet review: 3300698
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Abstract: A random group contains many quasiconvex surface subgroups.


References [Enhancements On Off] (What's this?)

  • [1] Agol I., The virtual Haken conjecture, available at arXiv:1204.2810. with an appendix with D. Groves and J. Manning.
  • [2] Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486 (2000k:53038)
  • [3] Danny Calegari and Alden Walker, Random rigidity in the free group, Geom. Topol. 17 (2013), no. 3, 1707-1744. MR 3073933, https://doi.org/10.2140/gt.2013.17.1707
  • [4] Calegari D. and Walker A. scallop, Computer program available from the authors' webpages.
  • [5] Calegari D. and Walker A., Surface subgroups from linear programming, available at arXiv:1212.2618.
  • [6] Calegari D. and Wilton H., Random graphs of free groups contain surface subgroups, available at arXiv:1303.2700.
  • [7] François Dahmani, Vincent Guirardel, and Piotr Przytycki, Random groups do not split, Math. Ann. 349 (2011), no. 3, 657-673. MR 2755002 (2012b:20101), https://doi.org/10.1007/s00208-010-0532-4
  • [8] M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1-295. MR 1253544 (95m:20041)
  • [9] Gromov M., personal communication.
  • [10] Jeremy Kahn and Vladimir Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold, Ann. of Math. (2) 175 (2012), no. 3, 1127-1190. MR 2912704, https://doi.org/10.4007/annals.2012.175.3.4
  • [11] Marcin Kotowski and Michał Kotowski, Random groups and property $ (T)$: Żuk's theorem revisited, J. Lond. Math. Soc. (2) 88 (2013), no. 2, 396-416. MR 3106728, https://doi.org/10.1112/jlms/jdt024
  • [12] Liu Y. and Markovic V., Homology of curves and surfaces in closed hyperbolic 3-manifolds, available at arXiv:1309.7418.
  • [13] Yann Ollivier, Some small cancellation properties of random groups, Internat. J. Algebra Comput. 17 (2007), no. 1, 37-51. MR 2300404 (2008g:20096), https://doi.org/10.1142/S021819670700338X
  • [14] Yann Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos [Mathematical Surveys], vol. 10, Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. MR 2205306 (2007e:20088)
  • [15] Yann Ollivier and Daniel T. Wise, Cubulating random groups at density less than $ 1/6$, Trans. Amer. Math. Soc. 363 (2011), no. 9, 4701-4733. MR 2806688 (2012e:20095), https://doi.org/10.1090/S0002-9947-2011-05197-4
  • [16] John R. Stallings, Topology of finite graphs, Invent. Math. 71 (1983), no. 3, 551-565. MR 695906 (85m:05037a), https://doi.org/10.1007/BF02095993
  • [17] A. Żuk, Property (T) and Kazhdan constants for discrete groups, Geom. Funct. Anal. 13 (2003), no. 3, 643-670. MR 1995802 (2004m:20079), https://doi.org/10.1007/s00039-003-0425-8

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Additional Information

Danny Calegari
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: dannyc@math.uchicago.edu

Alden Walker
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: akwalker@math.uchicago.edu

DOI: https://doi.org/10.1090/S0894-0347-2014-00802-X
Received by editor(s): April 5, 2013
Received by editor(s) in revised form: November 19, 2013, December 17, 2013, and January 27, 2014
Published electronically: June 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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