Volume 18, issue 1 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
A characterization for asymptotic dimension growth

Goulnara Arzhantseva, Graham A Niblo, Nick Wright and Jiawen Zhang

Algebraic & Geometric Topology 18 (2018) 493–524
Bibliography
1 J Behrstock, M F Hagen, A Sisto, Hierarchically hyperbolic spaces, I: Curve complexes for cubical groups, preprint (2014) arXiv:1412.2171
2 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
3 G C Bell, Growth of the asymptotic dimension function for groups, preprint (2005) arXiv:math/0504577
4 G Bell, A Dranishnikov, Asymptotic dimension in Bȩdlewo, Topology Proc. 38 (2011) 209 MR2725304
5 G C Bell, K Fujiwara, The asymptotic dimension of a curve graph is finite, J. Lond. Math. Soc. 77 (2008) 33 MR2389915
6 M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups, preprint (2010) arXiv:1006.1939
7 B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
8 B H Bowditch, Embedding median algebras in products of trees, Geom. Dedicata 170 (2014) 157 MR3199482
9 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
10 N P Brown, N Ozawa, C–algebras and finite-dimensional approximations, 88, Amer. Math. Soc. (2008) MR2391387
11 S Campbell, G A Niblo, Hilbert space compression and exactness of discrete groups, J. Funct. Anal. 222 (2005) 292 MR2132393
12 I Chatterji, G Niblo, From wall spaces to CAT(0) cube complexes, Internat. J. Algebra Comput. 15 (2005) 875 MR2197811
13 V Chepoi, Graphs of some CAT(0) complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
14 A N Dranishnikov, Groups with a polynomial dimension growth, Geom. Dedicata 119 (2006) 1 MR2247644
15 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
16 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
17 J R Isbell, Median algebra, Trans. Amer. Math. Soc. 260 (1980) 319 MR574784
18 V A Kaimanovich, Boundary amenability of hyperbolic spaces, from: "Discrete geometric analysis" (editors M Kotani, T Shirai, T Sunada), Contemp. Math. 347, Amer. Math. Soc. (2004) 83 MR2077032
19 G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621 MR1604899
20 B Nica, Cubulating spaces with walls, Algebr. Geom. Topol. 4 (2004) 297 MR2059193
21 P W Nowak, G Yu, Large scale geometry, Eur. Math. Soc. (2012) MR2986138
22 I Oppenheim, An intermediate quasi-isometric invariant between subexponential asymptotic dimension growth and Yu’s property A, Internat. J. Algebra Comput. 24 (2014) 909 MR3278391
23 N Ozawa, Metric spaces with subexponential asymptotic dimension growth, Internat. J. Algebra Comput. 22 (2012) MR2903746
24 L D Reeves, Biautomatic structures and combinatorics for cube complexes, PhD thesis, University of Melbourne (1995)
25 J Roe, Hyperbolic groups have finite asymptotic dimension, Proc. Amer. Math. Soc. 133 (2005) 2489 MR2146189
26 M Roller, Poc sets, median algebras and group actions : an extended study of Dunwoody’s construction and Sageev’s theorem, preprint (2016) arXiv:1607.07747
27 M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
28 J Smith, The asymptotic dimension of the first Grigorchuk group is infinity, Rev. Mat. Complut. 20 (2007) 119 MR2310581
29 J Spakula, N Wright, Coarse medians and Property A, preprint (2016) arXiv:1602.06084
30 N Wright, Finite asymptotic dimension for CAT(0) cube complexes, Geom. Topol. 16 (2012) 527 MR2916293
31 G Yu, The Novikov conjecture for groups with finite asymptotic dimension, Ann. of Math. 147 (1998) 325 MR1626745
32 G Yu, The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math. 139 (2000) 201 MR1728880
33 R. Zeidler, Coarse median structures on groups, Master’s thesis, University of Vienna (2013)