Algebraic & Geometric Topology 2 (2002) 921–936

DOI: 10.2140/agt.2002.2.921

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', Γ_K. We show that Γ_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

Mathematical Subject Classification

Primary: 20F67

Secondary: 57M20

References

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Publication

Received: 6 May 2002
Revised: 16 September 2002
Accepted: 12 October 2002
Published: 21 October 2002

Authors