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Peer-reviewedCC BYBulletin of the London Mathematical Society

The Haagerup property is not invariant under quasi‐isometry

  • Mathieu Carette1
  • Kevin Whyte2
  • Sylvain Arnt3
  • Thibault Pillon4
  • Alain Valette5
5 affiliations
  1. 1Rockestate SRL Brussels Belgium
  2. 2Dept. of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago Illinois USA
  3. 3Pôle Sup' Sainte Croix ‐ Saint Euverte Orléans France
  4. 4Haute école d'Ingénierie et de Gestion du Canton de Vaud Yverdon‐les‐Bains Switzerland
  5. 5Institut de Mathématiques, UniMail Neuchâtel Switzerland
Open at sourceDOICite

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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Cite

BibTeXRIS
BibTeX
@article{carette2026haagerup,
  title = {{The Haagerup property is not invariant under quasi‐isometry}},
  author = {Mathieu Carette and Kevin Whyte and Sylvain Arnt and Thibault Pillon and Alain Valette},
  journal = {Bulletin of the London Mathematical Society},
  year = {2026},
  month = oct,
  doi = {10.1112/blms.70516},
  url = {https://doi.org/10.1112/blms.70516},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - The Haagerup property is not invariant under quasi‐isometry
AU  - Mathieu Carette
AU  - Kevin Whyte
AU  - Sylvain Arnt
AU  - Thibault Pillon
AU  - Alain Valette
PY  - 2026
DA  - 2026/10/15
JO  - Bulletin of the London Mathematical Society
DO  - 10.1112/blms.70516
UR  - https://doi.org/10.1112/blms.70516
AB  - 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.
SN  - 0024-6093
SN  - 1469-2120
ER  -