# An uncountable family of non orbit equivalent actions of F_n

## D. Gaboriau, S. Popa

### J. Amer. Math. Soc.,  18  (2005),  547-559.

link to Journal of the American Mathematical Society

## Abstract

For each 1≤ n ≤∞,  we construct an uncountable family of free ergodic measure preserving actions alpha_t of the free group Fn on the standard probability space (X,µ) such that any two are non orbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid'' (in the sense of [Po01]), with the II_1 factors L^∞(X, µ)\rtimes_{alpha_t} Fn mutually non-isomorphic (even non-stably isomorphic) and in the class HTs.

## Abstract

Last modification : may 20, 2005