Highly faithful actions and dense free subgroups in full groups
Group Theory
2017-03-10 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1509.03584,
title = {Highly faithful actions and dense free subgroups in full groups},
author = {François Le Maître},
journal= {arXiv preprint arXiv:1509.03584},
year = {2017}
}
Comments
New version incorporating referee's comments. To appear in Groups, Geometry and Dynamics