Quasi-isometric rigidity of a class of right-angled Coxeter groups

Jordan Bounds; Xiangdong Xie

Quasi-isometric rigidity of a class of right-angled Coxeter groups

Group Theory 2018-10-04 v2

Authors: Jordan Bounds , Xiangdong Xie

Abstract

We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $\Gamma_1,\Gamma_2$ be joins of finite generalized thick $m$ -gons with $m\geq 3$ . We show that the corresponding right-angled Coxeter groups are quasi-isometric if and only if $\Gamma_1,\Gamma_2$ are isomorphic. We also give a construction of commensurable right-angled Coxeter groups.

Keywords

quasi-isometric rigidity right-angled coxeter groups generalized thick polygons join commensurable groups

Cite

@article{arxiv.1804.03123,
  title  = {Quasi-isometric rigidity of a class of right-angled Coxeter groups},
  author = {Jordan Bounds and Xiangdong Xie},
  journal= {arXiv preprint arXiv:1804.03123},
  year   = {2018}
}

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