The Haagerup property is not invariant under quasi‐isometry
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Abstract
Abstract Using the work of Cornulier–Valette and Whyte (see Appendix A for the latter), we show that neither the Haagerup property nor weak amenability is invariant under quasi‐isometry of finitely generated groups. Appendix B shows, using the same examples, that the same holds for vanishing of the equivariant ‐compression.
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View paper (DOI)Open access versionOpenAlexBulletin of the London Mathematical SocietyPublished 2026-10-15
Authors: Mathieu Carette, Sylvain Arnt, Thibault Pillon, Alain Valette
Institutions: University of Illinois Chicago, Haute École Pédagogique du Canton de Vaud, University of Neuchâtel