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A converse to Dye's theorem


Author: Greg Hjorth
Journal: Trans. Amer. Math. Soc. 357 (2005), 3083-3103
MSC (2000): Primary 03E15, 28D15, 37A15
DOI: https://doi.org/10.1090/S0002-9947-04-03672-4
Published electronically: July 22, 2004
MathSciNet review: 2135736
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Abstract: Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of $\mathbb{F} _2$ on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the $\leq_B$ ordering.


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Additional Information

Greg Hjorth
Affiliation: Department of Mathematics, University of California—Los Angeles, Los Angeles, California 90095-1555
Email: greg@math.ucla.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03672-4
Keywords: Ergodic theory, treeable equivalence relations, non-amenable groups, property $T$ groups, free groups, Borel reducibility
Received by editor(s): September 8, 2003
Published electronically: July 22, 2004
Additional Notes: The author was partially supported by NSF grant DMS 01-40503
Article copyright: © Copyright 2004 American Mathematical Society

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