Algebraic and Geometric Topology 2 (2002),
paper no. 37, pages 921-936.
On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups
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.
Nonpositive curvature, dimension, flag complex, Artin group
AMS subject classification.
Submitted: 6 May 2002.
(Revised: 16 September 2002.)
Accepted: 12 October 2002.
Published: 21 October 2002.
Notes on file formats
Laboratoire de Topologie, Universite de Bourgogne
UMR 5584 du CNRS - BP 47 870, 21078 Dijon, France
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