Using recent techniques introduced by Jones, we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if is a discrete group with the Haagerup property, then the permutational restricted wreath product obtained from the group and the usual action of Richard Thompson's group on the dyadic rational of the unit interval has the Haagerup property.
Cite this article
Arnaud Brothier, Haagerup property for wreath products constructed with Thompson's groups. Groups Geom. Dyn. 17 (2023), no. 2, pp. 671–718DOI 10.4171/GGD/714