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2002 On the CAT(0) dimension of 2–dimensional Bestvina–Brady groups
John Crisp
Algebr. Geom. Topol. 2(2): 921-936 (2002). DOI: 10.2140/agt.2002.2.921

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.

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John Crisp. "On the CAT(0) dimension of 2–dimensional Bestvina–Brady groups." Algebr. Geom. Topol. 2 (2) 921 - 936, 2002. https://doi.org/10.2140/agt.2002.2.921

Information

Received: 6 May 2002; Revised: 16 September 2002; Accepted: 12 October 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1055.20036
MathSciNet: MR1936975
Digital Object Identifier: 10.2140/agt.2002.2.921

Subjects:
Primary: 20F67
Secondary: 57M20

Rights: Copyright © 2002 Mathematical Sciences Publishers

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