Quasi-isometry and commensurability classification of certain right-angled Coxeter groups
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Bowditch's JSJ tree is a quasi-isometry invariant for one-ended hyperbolic groups, which uses the local cut point structure of their visual boundary. We compute this tree for a large family of hyperbolic right-angled Coxeter groups, and identify a subfamily for which this tree is a complete quasi-isometry invariant. We then investigate the commensurability classification of groups in this subfamily. For our work on commensurability, a key step is proving that these Coxeter groups are virtually geometric amalgams of surfaces. This is joint work with Pallavi Dani (Louisiana State University) and Emily Stark (University of Haifa).
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