Simple and large equivalence relations

Lewis Bowen

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arXiv · 1507.04841

Simple and large equivalence relations

Lewis Bowen

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Abstract

We construct ergodic discrete probability measure preserving equivalence relations $\cR$ that has 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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Lewis Bowen. 2015-08-09. Simple and large equivalence relations. https://arxiv.org/abs/1507.04841

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