A non-trivial example of a free-by-free group with the Haagerup property

Francois Gautero (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a fi nite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfi es the Haagerup property.

Mots clés: Haagerup property; a-T-menability; free groups; semidirect products

Domaines: Théorie des groupes [math.GR]

Francois Gautero. A non-trivial example of a free-by-free group with the Haagerup property. Groups, Geometry, and Dynamics, 2012, 6 (4), pp.677-699. ⟨hal-00768991⟩