Abstract
We prove that for a fairly large family of HNN extensions Γ, the group measure space II_1 factor L^\infty(X) \rtimes Γgiven by an arbitrary free ergodic probability measure preserving action of Γ, has a unique group measure space Cartan subalgebra up to unitary conjugacy. We deduce from this new examples of W^*-superrigid group actions, i.e. where the II_1 factor L^\infty(X) \rtimes Γentirely remembers the group action that it was constructed from.
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