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


Authors: Jordan Bounds and Xiangdong Xie
Journal: Proc. Amer. Math. Soc. 148 (2020), 553-568
MSC (2010): Primary 20F67, 20F65
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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Additional Information

Jordan Bounds
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403
Address at time of publication: Department of Mathematics, Furman University, Greenville, South Carolina 29613
Email: jordan.bounds@furman.edu

Xiangdong Xie
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403
Email: xiex@bgsu.edu

DOI: https://doi.org/10.1090/proc/14743
Received by editor(s): October 2, 2018
Received by editor(s) in revised form: June 17, 2019
Published electronically: August 7, 2019
Additional Notes: The second author acknowledges support from Simons Foundation grant #315130.
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2019 American Mathematical Society