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2012 Finite asymptotic dimension for $\mathrm{CAT}(0)$ cube complexes
Nick Wright
Geom. Topol. 16(1): 527-554 (2012). 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.

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Nick Wright. "Finite asymptotic dimension for $\mathrm{CAT}(0)$ cube complexes." Geom. Topol. 16 (1) 527 - 554, 2012. https://doi.org/10.2140/gt.2012.16.527

Information

Received: 12 July 2010; Revised: 12 January 2012; Accepted: 23 September 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1327.20047
MathSciNet: MR2916293
Digital Object Identifier: 10.2140/gt.2012.16.527

Subjects:
Primary: 20F65, 20F69, 54F45

Rights: Copyright © 2012 Mathematical Sciences Publishers

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