most citedThe Haagerup property is not invariant under quasi-isometry

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math.GR2026

Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric

Daniel Groves, Emily Stark, Genevieve S. Walsh +1

We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-iso…

math.GR2026★ 4 cited

The Haagerup property is not invariant under quasi-isometry

Mathieu Carette, Kevin Whyte, Sylvain Arnt +2

Using the work of Cornulier-Valette and Whyte, we show that neither the Haagerup property nor weak amenability is invariant under quasi-isometry of finitely generated groups.