Geodesic
On the CAT(0) dimension of 2–dimensional Bestvina–Brady groups
Crisp, John1
1Laboratoire de Topologie, Université de Bourgogne, UMR 5584 du CNRS, BP 47 870, 21078 Dijon, France
Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 921-936
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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.

DOI : 10.2140/agt.2002.2.921
Keywords: nonpositive curvature, dimension, flag complex, Artin group

Crisp, John  1

1 Laboratoire de Topologie, Université de Bourgogne, UMR 5584 du CNRS, BP 47 870, 21078 Dijon, France 
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Crisp, John. On the CAT(0) dimension of 2–dimensional Bestvina–Brady groups. Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 921-936. doi: 10.2140/agt.2002.2.921

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