Rigidity of warped cones and coarse geometry of expanders

Wouter Van Limbeek
University of Michigan

Finitely generated subgroups of compact Lie groups give rise to expander graphs via a warped cone construction. We study the dependence of the coarse geometry of such expander graphs on the original subgroup and establish a dynamical analogue of quasi-isometric rigidity theorems in geometric group theory: Namely, the coarse geometry of the warped cone determines the subgroup up to commensurability, unless the group has abelian factors. This produces many explicit examples of expanders with different geometry. This is joint work with Thang Nguyen and David Fisher.

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