Geometry & Topology Volume 23, issue 5 (2019)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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On the asymptotic dimension of the curve complex

Mladen Bestvina and Ken Bromberg

Geometry & Topology 23 (2019) 2227–2276

DOI: 10.2140/gt.2019.23.2227

Bibliography

1	I Agol, Ideal triangulations of pseudo-Anosov mapping tori, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 1 MR2866919
2	T Aougab, Quadratic bounds on the quasiconvexity of nested train track sequences, Topology Proc. 44 (2014) 365 MR3173789
3	J Behrstock, M F Hagen, A Sisto, Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups, Proc. Lond. Math. Soc. 114 (2017) 890 MR3653249
4	G C Bell, K Fujiwara, The asymptotic dimension of a curve graph is finite, J. Lond. Math. Soc. 77 (2008) 33 MR2389915
5	M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 1 MR3415065
6	M Bonk, O Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000) 266 MR1771428
7	B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
8	S V Buyalo, Asymptotic dimension of a hyperbolic space and the capacity dimension of its boundary at infinity, Algebra i Analiz 17 (2005) 70 MR2159584
9	S V Buyalo, Capacity dimension and embedding of hyperbolic spaces into the product of trees, Algebra i Analiz 17 (2005) 42 MR2173936
10	S V Buyalo, N D Lebedeva, Dimensions of locally and asymptotically self-similar spaces, Algebra i Analiz 19 (2007) 60 MR2319510
11	D Gabai, On the topology of ending lamination space, Geom. Topol. 18 (2014) 2683 MR3285223
12	É Ghys, P de la Harpe, Sur les groupes hyperboliques d’après Mikhael Gromov, 83, Birkhäuser (1990) MR1086657
13	B Grünbaum, Convex polytopes, 221, Springer (2003) MR1976856
14	U Hamenstädt, Geometry of the mapping class groups, I : Boundary amenability, Invent. Math. 175 (2009) 545 MR2471596
15	J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157 MR830043
16	S Hensel, P Przytycki, The ending lamination space of the five-punctured sphere is the Nöbeling curve, J. Lond. Math. Soc. 84 (2011) 103 MR2819692
17	D Hume, Embedding mapping class groups into a finite product of trees, Groups Geom. Dyn. 11 (2017) 613 MR3668054
18	E Klarreich, The boundary at infinity of the curve complex and the relative Teichmüller space, preprint (2018) arXiv:1803.10339
19	U Lang, T Schlichenmaier, Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions, Int. Math. Res. Not. 2005 (2005) 3625 MR2200122
20	J M Mackay, A Sisto, Embedding relatively hyperbolic groups in products of trees, Algebr. Geom. Topol. 13 (2013) 2261 MR3073916
21	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
22	H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
23	H A Masur, Y N Minsky, Quasiconvexity in the curve complex, from: "In the tradition of Ahlfors and Bers, III" (editors W Abikoff, A Haas), Contemp. Math. 355, Amer. Math. Soc. (2004) 309 MR2145071
24	R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
25	M Sapir, A Higman embedding preserving asphericity, J. Amer. Math. Soc. 27 (2014) 1 MR3110794
26	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
27	R C H Webb, Combinatorics of tight geodesics and stable lengths, Trans. Amer. Math. Soc. 367 (2015) 7323 MR3378831
28	G M Ziegler, Lectures on polytopes, 152, Springer (1995) MR1311028