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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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An uncountable family of nonorbit equivalent actions of $\mathbb {F}_n$
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by Damien Gaboriau and Sorin Popa PDF
J. Amer. Math. Soc. 18 (2005), 547-559 Request permission


For each $2 \leq n \leq \infty$, we construct an uncountable family of free ergodic measure preserving actions $\alpha _t$ of the free group $\mathbb {F}_n$ on the standard probability space $(X, \mu )$ such that any two are nonorbit equivalent (in fact, not even stably orbit equivalent). These actions are all “rigid” (in the sense of Popa), with the II$_1$ factors $L^\infty (X, \mu )\rtimes _{\alpha _t} \mathbb {F}_n$ mutually nonisomorphic (even nonstably isomorphic) and in the class $\mathcal {H}\mathcal {T}_{_{s}}.$
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Additional Information
  • Damien Gaboriau
  • Affiliation: Umpa, UMR CNRS 5669, ENS-Lyon, F-69364 Lyon Cedex 7, France
  • Email:
  • Sorin Popa
  • Affiliation: Department of Mathematics, Univeristy of California, Los Angeles, California 90095-1555
  • MR Author ID: 141080
  • Email:
  • Received by editor(s): September 12, 2003
  • Published electronically: March 28, 2005
  • Additional Notes: The first author wishes to thank the C.N.R.S
    The second author was supported in part by NSF Grant 0100883
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 18 (2005), 547-559
  • MSC (2000): Primary 37A20, 46L10
  • DOI:
  • MathSciNet review: 2138136