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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A characterization for asymptotic dimension growth

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

Algebraic & Geometric Topology 18 (2018) 493–524
Abstract

We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of Wright’s result on their finite asymptotic dimension. We also apply our new characterization to geodesic coarse median spaces of finite rank and establish that they have subexponential asymptotic dimension growth. This strengthens a recent result of S̆pakula and Wright.

Keywords
asymptotic dimension growth, CAT(0) cube complex, coarse median space, mapping class group
Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 20F69, 51F99
References
Publication
Received: 6 January 2017
Revised: 30 May 2017
Accepted: 29 June 2017
Published: 10 January 2018
Authors
Goulnara Arzhantseva
Universität Wien
Fakultät für Mathematik
Vienna
Austria
Graham A Niblo
School of Mathematics
University of Southampton
Southampton
United Kingdom
Nick Wright
Department of Mathematical Sciences
University of Southampton
Southampton
United Kingdom
Jiawen Zhang
School of Mathematics
University of Southampton
Southampton
United Kingdom