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Compact actions and uniqueness of the group measure space decomposition of II$_1$ factors (1112.0831v1)
Published 5 Dec 2011 in math.OA, math.FA, and math.GR
Abstract: We prove that any II$_1$ factor $L{\infty}(X)\rtimes\Gamma$ arising from a compact, free, ergodic, probability measure preserving action of a countable group $\Gamma$ with positive first $\ell2$-Betti number, has a unique group measure space Cartan subalgebra, up to unitary conjugacy.
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