Groups, Geometry, and Dynamics


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Volume 6, Issue 4, 2012, pp. 677–699
DOI: 10.4171/GGD/170

Published online: 2012-11-10

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

François Gautero[1]

(1) Université de Nice Sophia Antipolis, Nice, France

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.

Keywords: Haagerup property, a-T-menability, free groups, semidirect products

Gautero François: A non-trivial example of a free-by-free group with the Haagerup property. Groups Geom. Dyn. 6 (2012), 677-699. doi: 10.4171/GGD/170