Finite asymptotic dimension for CAT(0) cube complexes

Wright, Nick

doi:10.2140/gt.2012.16.527

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Finite asymptotic dimension for $\mathrm{CAT}(0)$ cube complexes

Nick Wright

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, $\mathrm{CAT}(0)$ cube complex, small cancellation group

Mathematical Subject Classification 2000

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

Nick Wright
Mathematics University of Southampton University Road Southampton SO17 1BJ UK

Volume 16, issue 1 (2012)