Finite asymptotic dimension for CAT(0) cube complexes

Wright, Nick¹

¹ Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ, UK

Geometry & topology, Tome 16 (2012) no. 1, pp. 527-554.

Résumé

We prove that the asymptotic dimension of a finite-dimensional $CAT\left(0\right)$ 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 $CAT\left(0\right)$ 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.

Détail

DOI : 10.2140/gt.2012.16.527

Keywords: asymptotic dimension, $\mathrm{CAT}(0)$ cube complex, small cancellation group

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