The number of topological generators for full groups of ergodic equivalence relations

François Le Maître (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We completely elucidate the relationship between two invariants associated with an ergodic probability measure-preserving (pmp) equivalence relation, namely its cost and the minimal number of topological generators of its full group. It follows that for any free pmp ergodic action of the free group on $n$ generators, the minimal number of topological generators for the full group of the action is $n+1$, answering a question of Kechris.

Keywords: full group; topological generators; cost; pmp equivalence relation

Domains: Mathematics [math]; Dynamical Systems [math.DS]; Mathematics [math]; Group Theory [math.GR]

François Le Maître. The number of topological generators for full groups of ergodic equivalence relations. Inventiones Mathematicae, 2014, pp.261-268. ⟨10.1007/s00222-014-0503-6⟩. ⟨ensl-00787328⟩