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An uncountable family of nonorbit equivalent actions of $\mathbb {F}_n$


Authors: Damien Gaboriau and Sorin Popa
Journal: J. Amer. Math. Soc. 18 (2005), 547-559
MSC (2000): Primary 37A20, 46L10
DOI: https://doi.org/10.1090/S0894-0347-05-00480-7
Published electronically: March 28, 2005
MathSciNet review: 2138136
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Abstract: 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: gaboriau@umpa.ens-lyon.fr

Sorin Popa
Affiliation: Department of Mathematics, Univeristy of California, Los Angeles, California 90095-1555
MR Author ID: 141080
Email: popa@math.ucla.edu

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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.