A Measurable-Group-Theoretic Solution to von Neumann's Problem

Damien Gaboriau (1) , Russell Lyons (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Department of Mathematics, Indiana University

We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors.

Mots clés: trees; graphs; percolation theory; von Neumann's problem; Orbit equivalence; free group; non-amenability

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

Damien Gaboriau, Russell Lyons. A Measurable-Group-Theoretic Solution to von Neumann's Problem. Inventiones Mathematicae, 2009, 177 (3), pp.533-540. ⟨10.1007/s00222-009-0187-5⟩. ⟨hal-00186658v2⟩