arXiv subjects
Publications and source records attributed to An Speelman.
We construct a group measure space II$_1$ factor that has two non-conjugate Cartan subalgebras. We show that the fundamental group of the II$_1$ factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is non-trivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.
We construct a class of II_1 factors M that admit unclassifiably many Cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of M is complete analytic, in particular non Borel. We also construct a II_1 factor that admits uncountably many non isomorphic group measure space decompositions, all involving the same group G. So G is a group that admits uncountably many non stably orbit equivalent actions whose crossed product II_1 factors are all isomorphic.