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An uncountable family of nonorbit equivalent actions of
Authors:Damien Gaboriau   Sorin Popa
Affiliation:Umpa, UMR CNRS 5669, ENS-Lyon, F-69364 Lyon Cedex 7, France ; Department of Mathematics, Univeristy of California, Los Angeles, California 90095-1555
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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