Finite asymptotic dimension for CAT(0) cube complexes
Metric Geometry
2014-11-11 v2 Group Theory
Abstract
In this paper we prove that the asymptotic dimension of a finite-dimensional CAT(0) cube complex is bounded above by the dimension. To achieve this we prove a controlled colouring theorem for the complex. We also show that every CAT(0) cube complex is a contractive retraction of an infinite dimensional cube. As an example of the dimension theorem we obtain bounds on the asymptotic dimension of small cancellation groups.
Cite
@article{arxiv.1004.4172,
title = {Finite asymptotic dimension for CAT(0) cube complexes},
author = {Nick Wright},
journal= {arXiv preprint arXiv:1004.4172},
year = {2014}
}