Highly faithful actions and dense free subgroups in full groups
arXiv:1509.03584
Abstract
In this paper, we show that every measure-preserving ergodic equivalence relation of cost less than m comes from a "rich" faithful invariant random subgroup of the free group on m generators, strengthening a result of Bowen which had been obtained by a Baire category argument. Our proof is completely explicit: we use our previous construction of topological generators for full groups and observe that these generators induce a totally non free action. We then twist this construction so that the action is moreover amenable onto almost every orbit and highly faithful.
New version incorporating referee's comments. To appear in Groups, Geometry and Dynamics