Failure of quasi-isometric rigidity for infinite-ended groups

Nir Lazarovich, Emily Stark

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationTopology at Infinity of Discrete Groups - AMS Special Session on Ends and Boundaries of Groups In honor of Michael Mihalik’s 70th Birthday, 2023
EditorsRoss Geoghegan, Craig R. Guilbault, Kim Ruane
PublisherAmerican Mathematical Society
Pages297-304
Number of pages8
ISBN (Print)9781470478636
DOIs
StatePublished - 2025
EventAMS Special Session on Ends and Boundaries of Groups In honor of Michael Mihalik’s 70th Birthday, 2023 - Cincinnati, United States
Duration: 15 Apr 202316 Apr 2023

Publication series

NameContemporary Mathematics
Volume812

Conference

ConferenceAMS Special Session on Ends and Boundaries of Groups In honor of Michael Mihalik’s 70th Birthday, 2023
Country/TerritoryUnited States
CityCincinnati
Period15/04/2316/04/23

All Science Journal Classification (ASJC) codes

  • General Mathematics

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