Simple and large equivalence relations
Abstract
We construct ergodic discrete probability measure preserving equivalence relations 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 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.
Keywords
Cite
@article{arxiv.1507.04841,
title = {Simple and large equivalence relations},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:1507.04841},
year = {2015}
}
Comments
Comments welcome! This new version includes expanded reference to previous work of Stefaan Vaes which constructs equivalence relations without finite extensions or ergodic finite index sub relations. Also I shortened the paper by removing my construction with Pierre-Emmanuel Caprace since Stefaan's constructions are based on the same principles