#### Volume 18, issue 3 (2018)

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Divergence of $\mathrm{CAT}(0)$ cube complexes and Coxeter groups

### Ivan Levcovitz

Algebraic & Geometric Topology 18 (2018) 1633–1673
##### Bibliography
 1 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553 2 P Bahls, The isomorphism problem in Coxeter groups, Imperial College Press (2005) MR2162146 3 J A Behrstock, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006) 1523 MR2255505 4 J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959 5 J Behrstock, C Druţu, Divergence, thick groups, and short conjugators, Illinois J. Math. 58 (2014) 939 MR3421592 6 J Behrstock, V Falgas-Ravry, M F Hagen, T Susse, Global structural properties of random graphs, Int. Math. Res. Not. (2016) 7 J Behrstock, M F Hagen, Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries, Groups Geom. Dyn. 10 (2016) 649 MR3513112 8 J Behrstock, M F Hagen, A Sisto, Thickness, relative hyperbolicity, and randomness in Coxeter groups, Algebr. Geom. Topol. 17 (2017) 705 MR3623669 9 A Björner, F Brenti, Combinatorics of Coxeter groups, 231, Springer (2005) MR2133266 10 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486 11 P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012 12 P Dani, A Thomas, Divergence in right-angled Coxeter groups, Trans. Amer. Math. Soc. 367 (2015) 3549 MR3314816 13 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474 14 M W Davis, T Januszkiewicz, Right-angled Artin groups are commensurable with right-angled Coxeter groups, J. Pure Appl. Algebra 153 (2000) 229 MR1783167 15 C Druţu, S Mozes, M Sapir, Divergence in lattices in semisimple Lie groups and graphs of groups, Trans. Amer. Math. Soc. 362 (2010) 2451 MR2584607 16 S M Gersten, Divergence in 3–manifold groups, Geom. Funct. Anal. 4 (1994) 633 MR1302334 17 S M Gersten, Quadratic divergence of geodesics in CAT(0) spaces, Geom. Funct. Anal. 4 (1994) 37 MR1254309 18 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, II" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544 19 D Gruber, A Sisto, Infinitely presented graphical small cancellation groups are acylindrically hyperbolic, preprint (2014) arXiv:1408.4488 20 M F Hagen, The simplicial boundary of a CAT(0) cube complex, Algebr. Geom. Topol. 13 (2013) 1299 MR3071129 21 M F Hagen, Weak hyperbolicity of cube complexes and quasi-arboreal groups, J. Topol. 7 (2014) 385 MR3217625 22 M Kapovich, B Leeb, 3–Manifold groups and nonpositive curvature, Geom. Funct. Anal. 8 (1998) 841 MR1650098 23 I Levcovitz, A quasi-isometry invariant and thickness bounds for right-angled Coxeter groups, preprint (2017) arXiv:1705.06416 24 N Macura, CAT(0) spaces with polynomial divergence of geodesics, Geom. Dedicata 163 (2013) 361 MR3032700 25 A Y Ol’shanskiĭ, Geometry of defining relations in groups, 70, Kluwer (1991) MR1191619 26 A Y Ol’shanskii, D V Osin, M V Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009) 2051 MR2507115 27 D T Wise, The structure of groups with a quasiconvex hierarchy, preprint (2011)