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arXiv:2310.03644 [math.GR]AbstractReferencesReviewsResources

Failure of quasi-isometric rigidity for infinite-ended groups

Nir Lazarovich, Emily Stark

Published 2023-10-05Version 1

We prove that an infinite-ended group whose one-ended factors have finite-index subgroups and are in a family of groups with a nonzero multiplicative invariant is not quasi-isometrically rigid. Combining this result with work of the first author proves that a residually-finite multi-ended hyperbolic group is quasi-isometrically rigid if and only if it is virtually free. The proof adapts an argument of Whyte for commensurability of free products of closed hyperbolic surface groups.

Comments: 8 pages
Categories: math.GR, math.GT
Subjects: 20F65, 20E08, 20F67
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