Geometry & Topology 16 (2012) 527–554

DOI: 10.2140/gt.2012.16.527

Abstract

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.

Keywords

asymptotic dimension, CAT(0) cube complex, small cancellation group

Mathematical Subject Classification

Primary: 20F65, 20F69, 54F45

References

Publication

Received: 12 July 2010
Revised: 12 January 2012
Accepted: 23 September 2011
Published: 8 April 2012
Proposed: Martin Bridson
Seconded: Dmitri Burago, Steve Ferry

Authors