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arXiv · 1509.03584

Highly faithful actions and dense free subgroups in full groups

François Le Maître
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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.

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François Le Maître. 2015-09-11. Highly faithful actions and dense free subgroups in full groups. https://arxiv.org/abs/1509.03584

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