Examples of Groups that are Measure Equivalent to the Free Group

Damien Gaboriau (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.

Mots clés: random graphs; free products with amalgamation; free group; measured equivalence relations; measure equivalence; orbit equivalence

Domaines: Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]; Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Damien Gaboriau. Examples of Groups that are Measure Equivalent to the Free Group. Ergodic Theory and Dynamical Systems, 2005, 25 (6), pp.1809-1827. ⟨10.1017/S0143385705000258⟩. ⟨hal-00004408v2⟩