Simple and large equivalence relations

Bowen, Lewis

doi:10.1090/proc/13257

Simple and large equivalence relations
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Proc. Amer. Math. Soc. 145 (2017), 215-224 Request permission

Abstract:

We construct ergodic discrete probability-measure-preserving equivalence relations $\mathcal {R}$ that have no proper ergodic normal subequivalence relations and no proper ergodic finite-index subequivalence relations. We show that every treeable equivalence relation satisfying a mild ergodicity condition and cost $>1$ surjects onto every countable group with ergodic kernel. Lastly, we provide a simple characterization of normality for subequivalence relations and an algebraic description of the quotient.

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