#### Volume 18, issue 1 (2018)

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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 $CAT\left(0\right)$ 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