The Haagerup property is not invariant under quasi-isometry
arXiv:1403.5446
Abstract
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.
12 pages; Appendix A by Kevin Whyte; Appendix B by Sylvain Arnt, Thibault Pillon and Alain Valette