An Uncountable Family of Non Orbit Equivalent Actions of Fn
Damien Gaboriau, Sorin Popa
Abstract
For each 2 ≤ n ≤ ∞, we construct an uncountable family of free ergodic measure preserving actions αt 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 II1 factors L∞(X, μ)αt Fn mutually non stably isomorphic (even non-stably isomorphic) and in the class H T_s.
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