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Embedding relatively hyperbolic groups in products of trees

John M Mackay and Alessandro Sisto

Algebraic & Geometric Topology 13 (2013) 2261–2282
Bibliography
1 I Agol, Criteria for virtual fibering, J. Topol. 1 (2008) 269 MR2399130
2 M Aschenbrenner, S Friedl, H Wilton, 3-manifold groups arXiv:1205.0202
3 G Bell, A Dranishnikov, On asymptotic dimension of groups, Algebr. Geom. Topol. 1 (2001) 57 MR1808331
4 G Bell, A Dranishnikov, On asymptotic dimension of groups acting on trees, Geom. Dedicata 103 (2004) 89 MR2034954
5 G Bell, A Dranishnikov, A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory, Trans. Amer. Math. Soc. 358 (2006) 4749 MR2231870
6 M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups arXiv:1006.1939
7 B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016, 66 MR2922380
8 N Brodskiy, J Dydak, J Higes, A Mitra, Assouad–Nagata dimension via Lipschitz extensions, Israel J. Math. 171 (2009) 405 MR2520117
9 N Brodskiy, J Dydak, M Levin, A Mitra, A Hurewicz theorem for the Assouad–Nagata dimension, J. Lond. Math. Soc. 77 (2008) 741 MR2418302
10 N Brodskiy, J Higes, Assouad–Nagata dimension of tree-graded spaces arXiv:0910.2378
11 M Burger, A Iozzi, N Monod, Equivariant embeddings of trees into hyperbolic spaces, Int. Math. Res. Not. 2005 (2005) 1331 MR2152540
12 S Buyalo, Asymptotic dimension of a hyperbolic space and the capacity dimension of its boundary at infinity, Algebra i Analiz 17 (2005) 70 MR2159584
13 S Buyalo, Capacity dimension and embedding of hyperbolic spaces into the product of trees, Algebra i Analiz 17 (2005) 42 MR2173936
14 S Buyalo, A Dranishnikov, V Schroeder, Embedding of hyperbolic groups into products of binary trees, Invent. Math. 169 (2007) 153 MR2308852
15 S Buyalo, N Lebedeva, Dimensions of locally and asymptotically self-similar spaces, Algebra i Analiz 19 (2007) 60 MR2319510
16 S Buyalo, V Schroeder, Embedding of hyperbolic spaces in the product of trees, Geom. Dedicata 113 (2005) 75 MR2171299
17 S Buyalo, V Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich (2007) MR2327160
18 S Buyalo, V Shrëder, The hyperbolic dimension of metric spaces, Algebra i Analiz 19 (2007) 93 MR2319511
19 Y de Cornulier, Dimension of asymptotic cones of Lie groups, J. Topol. 1 (2008) 342 MR2399134
20 F Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003) 933 MR2026551
21 A Dranishnikov, On asymptotic dimension of amalgamated products and right-angled Coxeter groups, Algebr. Geom. Topol. 8 (2008) 1281 MR2443244
22 A Dranishnikov, Cohomological approach to asymptotic dimension, Geom. Dedicata 141 (2009) 59 MR2520063
23 A Dranishnikov, J Smith, On asymptotic Assouad–Nagata dimension, Topology Appl. 154 (2007) 934 MR2294641
24 C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
25 J Dydak, J Higes, Asymptotic cones and Assouad–Nagata dimension, Proc. Amer. Math. Soc. 136 (2008) 2225 MR2383529
26 B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810 MR1650094
27 Ś R Gal, Asymptotic dimension and uniform embeddings, Groups Geom. Dyn. 2 (2008) 63 MR2367208
28 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
29 D Groves, J F Manning, Dehn filling in relatively hyperbolic groups, Israel J. Math. 168 (2008) 317 MR2448064
30 J Higes, I Peng, Assouad–Nagata dimension of connected Lie groups, Math. Z. 273 (2013) 283 MR3010160
31 D Hume, Direct embeddings of relatively hyperbolic groups with optimal $\ell^p$ compression exponent arXiv:1111.6013
32 D Hume, Embedding mapping class groups into finite products of trees arXiv:1207.2132
33 D Hume, A Sisto, Embedding universal covers of graph manifolds in products of trees, to appear in Proc. Amer. Math. Soc. arXiv:1112.0263
34 I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory" (editors S Cleary, R Gilman, A G Myasnikov, V Shpilrain), Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
35 U Lang, T Schlichenmaier, Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions, Int. Math. Res. Not. 2005 (2005) 3625 MR2200122
36 Y Liu, Virtual cubulation of nonpositively curved graph manifolds arXiv:1110.1940
37 J M Mackay, A Sisto, Quasi-hyperbolic planes in relatively hyperbolic groups arXiv:1111.2499
38 P W Nowak, On exactness and isoperimetric profiles of discrete groups, J. Funct. Anal. 243 (2007) 323 MR2291440
39 D Osin, Asymptotic dimension of relatively hyperbolic groups, Int. Math. Res. Not. 2005 (2005) 2143 MR2181790
40 S D Pauls, The large scale geometry of nilpotent Lie groups, Comm. Anal. Geom. 9 (2001) 951 MR1883722
41 P Przytycki, D T Wise, Mixed 3-manifolds are virtually special arXiv:1205.6742
42 A Sisto, Contracting elements and random walks arXiv:1112.2666
43 A Sisto, Projections and relative hyperbolicity, to appear in Enseign. Math. (2013)
44 S Wang, F Yu, Graph manifolds with non-empty boundary are covered by surface bundles, Math. Proc. Cambridge Philos. Soc. 122 (1997) 447 MR1466648
45 D Wise, The structure of groups with a quasiconvex hierarchy (2011)
46 D T Wise, From riches to raags: 3-manifolds, right-angled Artin groups, and cubical geometry, CBMS Regional Conference Series in Mathematics 117, Published for the Conference Board of the Mathematical Sciences (2012)