Algebraic and Geometric Topology 2 (2002), paper no. 37, pages 921-936.

On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

John Crisp

Abstract. Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. Different choices of K lead to examples where the CAT(0) dimension is 3, and either (i) the geometric dimension is 2, or (ii) the cohomological dimension is 2 and the geometric dimension is not known.

Keywords. Nonpositive curvature, dimension, flag complex, Artin group

AMS subject classification. Primary: 20F67. Secondary: 57M20.

DOI: 10.2140/agt.2002.2.921

E-print: arXiv:math.GR/0211130

Submitted: 6 May 2002. (Revised: 16 September 2002.) Accepted: 12 October 2002. Published: 21 October 2002.

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John Crisp
Laboratoire de Topologie, Universite de Bourgogne
UMR 5584 du CNRS - BP 47 870, 21078 Dijon, France
Email: jcrisp@u-bourgogne.fr

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