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Coarse geometry of expanders from rigidity of warped cones. (arXiv:1710.03085v1 [math.MG])
来源于:arXiv
We study quasi-isometry types of expanders that come from a warped cone
construction over group actions on homogeneous spaces. We prove a rigidity
theorem for the coarse geometry of such warped cones: Namely, if the group has
no abelian factors, then two such warped cones are quasi-isometric if and only
if the actions are conjugate in finite covers. As a consequence, we produce a
continuum 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 group. 查看全文>>