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Topological rigidity fails for quotients of the Davis complex


Author: Emily Stark
Journal: Proc. Amer. Math. Soc. 146 (2018), 5357-5366
MSC (2010): Primary 51F15; Secondary 20E07, 20F55, 20F67
DOI: https://doi.org/10.1090/proc/13809
Published electronically: September 4, 2018
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Abstract: A Coxeter group acts properly and cocompactly by isometries on the Davis complex for the group; we call the quotient of the Davis complex under this action the Davis orbicomplex for the group. We prove the set of finite covers of the Davis orbicomplexes for the set of one-ended Coxeter groups is not topologically rigid. We exhibit a quotient of a Davis complex by a one-ended right-angled Coxeter group which has two finite covers that are homotopy equivalent but not homeomorphic. We discuss consequences for the abstract commensurability classification of Coxeter groups.


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Emily Stark
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000 Israel

DOI: https://doi.org/10.1090/proc/13809
Received by editor(s): November 3, 2016
Received by editor(s) in revised form: May 3, 2017, and May 7, 2017
Published electronically: September 4, 2018
Additional Notes: The author was supported by the Azrieli Foundation and the Israel Science Foundation (grant 1941/14), and was supported in part at the Technion by a Zuckerman Fellowship.
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society

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