The aim of this note is to prove that the group of Formanek–Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies the Haagerup property.
Cite this article
François Gautero, A non-trivial example of a free-by-free group with the Haagerup property. Groups Geom. Dyn. 6 (2012), no. 4, pp. 677–699DOI 10.4171/GGD/170