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arXiv · 1710.03085

Rigidity of warped cones and coarse geometry of expanders

David Fisher·Thang Nguyen·Wouter van Limbeek
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Abstract

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups.

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BibTeXRIS

David Fisher, Thang Nguyen, Wouter van Limbeek. 2017-10-09. Rigidity of warped cones and coarse geometry of expanders. https://arxiv.org/abs/1710.03085

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