The Haagerup property is not invariant under quasi‐isometry
Bulletin of the London Mathematical Society, Volume 58, Issue 11, November 2026.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 Lp$L^p$‐compression.
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