A class of II_1 factors with exactly two group measure space decompositions

Abstract

We construct the first II_1 factors having exactly two group measure space decompositions up to unitary conjugacy. Also, for every positive integer $n$, we construct a II_1 factor $M$ that has exactly $n$ group measure space decompositions up to conjugacy by an automorphism.

v2: minor changes, final version, to appear in Journal de Mathématiques Pures et Appliquées