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An Uncountable Family of Non Orbit Equivalent Actions of $Bbb F_n$ | Damien Gaboriau
; Sorin Popa
; | Date: |
31 May 2003 | Subject: | Group Theory; Operator Algebras MSC-class: 28D15, 46L10, 46L35, 20E05 | math.GR math.OA | 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 $Bbb F_n$ on the standard probability space $(X, mu)$ 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 $L^infty(X, mu)
times_{alpha_t} Bbb F_n$ mutually non stably isomorphic (even non-stably isomorphic) and in the class $Cal HCal T_{_{s}}.$ | Source: | arXiv, math.GR/0306011 | Services: | Forum | Review | PDF | Favorites |
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