Bulletin of the London Mathematical Society· 2026Q1
The Haagerup property is not invariant under quasi‐isometry
- 4citations
- Q1SCImago
- 2026year
Short summary
The Haagerup property and weak amenability are not invariant under quasi-isometry for finitely generated groups.
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Key points
- The Haagerup property is not invariant under quasi-isometry for finitely generated groups.
- Weak amenability is also not invariant under quasi-isometry for finitely generated groups.
- Vanishing of equivariant L2-compression is not invariant under quasi-isometry.
- The findings are based on prior work by Cornulier-Valette and Whyte.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics