An uncountable family of nonorbit equivalent actions of 𝔽_{𝕟}

Gaboriau, Damien¹ ; Popa, Sorin²

¹ Umpa, UMR CNRS 5669, ENS-Lyon, F-69364 Lyon Cedex 7, France
² Department of Mathematics, Univeristy of California, Los Angeles, California 90095-1555

Journal of the American Mathematical Society, Tome 18 (2005) no. 3, pp. 547-559

Résumé

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 $\mathcal {H}\mathcal {T}_{_{s}}.$

Détail

DOI : 10.1090/S0894-0347-05-00480-7

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