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

Bounds, Jordan; Xie, Xiangdong

doi:10.1090/proc/14743

Quasi-isometric rigidity of a class of right-angled Coxeter groups
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by Jordan Bounds and Xiangdong Xie

Proc. Amer. Math. Soc. 148 (2020), 553-568

DOI: https://doi.org/10.1090/proc/14743

Published electronically: August 7, 2019

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Abstract:

We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $\Gamma _1$, $\Gamma _2$ be joins of finite thick generalized $m$-gons with $m\in \{3,4,6,8\}$. 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.

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