Mixed 3-manifolds are virtually special

Przytycki, Piotr¹ ; Wise, Daniel²

¹ Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland; and Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9
² Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9

Journal of the American Mathematical Society, Tome 31 (2018) no. 2, pp. 319-347

Résumé

Let $M$ be a compact oriented irreducible $3$-manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that $\pi _1M$ is virtually special.

Détail

DOI : 10.1090/jams/886

Bibliographie

[1] Agol, Ian Tameness of hyperbolic 3-manifolds 2004

[2] Agol, Ian Criteria for virtual fibering J. Topol. 2008 269 284

[3] Agol, Ian The virtual Haken conjecture Doc. Math. 2013 1045 1087

[4] Aschenbrenner, Matthias, Friedl, Stefan, Wilton, Henry 3-manifold groups 2015

[5] Bigdely, Hadi, Wise, Daniel T. Quasiconvexity and relatively hyperbolic groups that split Michigan Math. J. 2013 387 406

[6] Bonahon, Francis Bouts des variétés hyperboliques de dimension 3 Ann. of Math. (2) 1986 71 158

[7] Bonahon, Francis Geometric structures on 3-manifolds 2002 93 164

[8] Bridson, Martin R. On the subgroups of semihyperbolic groups 2001 85 111

[9] Calegari, Danny, Gabai, David Shrinkwrapping and the taming of hyperbolic 3-manifolds J. Amer. Math. Soc. 2006 385 446

[10] Canary, Richard D. A covering theorem for hyperbolic 3-manifolds and its applications Topology 1996 751 778

[11] Cooper, D., Long, D. D., Reid, A. W. Essential closed surfaces in bounded 3-manifolds J. Amer. Math. Soc. 1997 553 563

[12] Davis, Michael W., Januszkiewicz, Tadeusz Right-angled Artin groups are commensurable with right-angled Coxeter groups J. Pure Appl. Algebra 2000 229 235

[13] Gerasimov, Victor, Potyagailo, Leonid Quasiconvexity in relatively hyperbolic groups J. Reine Angew. Math. 2016 95 135

[14] Haglund, Frã©Dã©Ric, Wise, Daniel T. Special cube complexes Geom. Funct. Anal. 2008 1551 1620

[15] Haglund, Frã©Dã©Ric, Wise, Daniel T. Coxeter groups are virtually special Adv. Math. 2010 1890 1903

[16] Hamilton, Emily Abelian subgroup separability of Haken 3-manifolds and closed hyperbolic 𝑛-orbifolds Proc. London Math. Soc. (3) 2001 626 646

[17] Hruska, G. Christopher Relative hyperbolicity and relative quasiconvexity for countable groups Algebr. Geom. Topol. 2010 1807 1856

[18] Hruska, G. C., Wise, Daniel T. Finiteness properties of cubulated groups Compos. Math. 2014 453 506

[19] Hsu, Tim, Wise, Daniel T. On linear and residual properties of graph products Michigan Math. J. 1999 251 259

[20] Jankiewicz, Kasia The fundamental theorem of cubical small cancellation theory Trans. Amer. Math. Soc. 2017 4311 4346

[21] Kapovich, Michael Hyperbolic manifolds and discrete groups 2001

[22] Kronheimer, P. B., Mrowka, T. S. Dehn surgery, the fundamental group and SU(2) Math. Res. Lett. 2004 741 754

[23] Leeb, Bernhard 3-manifolds with(out) metrics of nonpositive curvature Invent. Math. 1995 277 289

[24] Liu, Yi Virtual cubulation of nonpositively curved graph manifolds J. Topol. 2013 793 822

[25] Martã­Nez-Pedroza, Eduardo Combination of quasiconvex subgroups of relatively hyperbolic groups Groups Geom. Dyn. 2009 317 342

[26] Minasyan, Ashot Separable subsets of GFERF negatively curved groups J. Algebra 2006 1090 1100

[27] Przytycki, Piotr, Wise, Daniel T. Graph manifolds with boundary are virtually special J. Topol. 2014 419 435

[28] Roller, Martin Poc sets, median algebras, and group actions. An extended study of Dunwoody’s construction and Sageev’s theorem. 1998

[29] Rubinstein, J. Hyam, Wang, Shicheng 𝜋₁-injective surfaces in graph manifolds Comment. Math. Helv. 1998 499 515

[30] Thurston, William P. The Geometry and Topology of Three-Manifolds 1980

[31] Thurston, William P. A norm for the homology of 3-manifolds Mem. Amer. Math. Soc. 1986

[32] Wise, Daniel T. From riches to raags: 3-manifolds, right-angled Artin groups, and cubical geometry 2012