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Finite asymptotic dimension for CAT(0) cube complexes (1004.4172v2)
Published 23 Apr 2010 in math.MG and math.GR
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.