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Simple and large equivalence relations


Author: Lewis Bowen
Journal: Proc. Amer. Math. Soc. 145 (2017), 215-224
MSC (2010): Primary 37A20, 37A15
DOI: https://doi.org/10.1090/proc/13257
Published electronically: July 25, 2016
MathSciNet review: 3565374
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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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Additional Information

Lewis Bowen
Affiliation: Department of Mathematics University of Hawai’i–Manoa, Honolulu, Hawaii

DOI: https://doi.org/10.1090/proc/13257
Keywords: Ergodic equivalence relations
Received by editor(s): August 18, 2015
Received by editor(s) in revised form: March 7, 2016
Published electronically: July 25, 2016
Additional Notes: This work was supported in part by NSF grant DMS-1500389, NSF CAREER Award DMS-0954606
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society