English

On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups

Group Theory 2014-10-01 v1 Geometric Topology

Abstract

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.

Keywords

Cite

@article{arxiv.math/0211130,
  title  = {On the CAT(0) dimension of 2-dimensional Bestvina-Brady groups},
  author = {John Crisp},
  journal= {arXiv preprint arXiv:math/0211130},
  year   = {2014}
}

Comments

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-37.abs.html