Finite asymptotic dimension for CAT(0) cube complexes

Details Finite asymptotic dimension for CAT(0) cube complexes Finite asymptotic dimension for CAT(0) cube complexes

2010-04-23

arxiv.org/abs/1004.4172v2

Mathematics

Metric Geometry

Scientific paper

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.

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