Volume 2, issue 2 (2002)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the CAT(0) dimension of 2–dimensional Bestvina–Brady groups

John Crisp

Algebraic & Geometric Topology 2 (2002) 921–936

arXiv: math.GR/0211130

Abstract

Let K be a 2–dimensional finite flag complex. We study the CAT(0) dimension of the ‘Bestvina–Brady group’, or ‘Artin kernel’, ΓK. We show that ΓK 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
Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 57M20
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Publication
Received: 6 May 2002
Revised: 16 September 2002
Accepted: 12 October 2002
Published: 21 October 2002
Authors
John Crisp
Laboratoire de Topologie
Université de Bourgogne
UMR 5584 du CNRS
BP 47 870
21078 Dijon
France