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

1804.03123Apr 9, 2018

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

Jordan Bounds, Xiangdong Xie

Abstract

We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $Γ_1,Γ_2$ be joins of finite generalized thick $m$ -gons with $m\geq 3$

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. We show that the corresponding right-angled Coxeter groups are quasi-isometric if and only if

Γ_1,Γ_2

are isomorphic. We also give a construction of commensurable right-angled Coxeter groups.

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