Motivated by Popa's seminal work Popa (Invent Math 165: 409-45, 2006), in this paper, we
provide a fairly large class of examples of group actions Γ\curvearrowright X Γ↷ X satisfying …

We introduce a new equivalence relation on groups, which we call von Neumann
equivalence, that is coarser than both measure equivalence and $ W^* $-equivalence. We …

In this paper, the notion of proper proximality (introduced in [BIP18]) is studied and classified
in various families of groups. We show that if a group acts non-elementarily by isometries on …

Using computations in the bidual of B (L 2 M) we develop a new technique at the von
Neumann algebra level to upgrade relative proper proximality to full proper proximality. This …

The notion of von Neumann equivalence (vNE), which encapsulates both measure
equivalence and W-equivalence, was introduced recently by Ishan, Peterson, and Ruth …

We here consider inner amenability from a geometric and group theoretical perspective. We
prove that for every non-elementary action of a group G on a finite dimensional irreducible …

We prove that for every $ N\ge 3$, the group $\mathrm {Out}(F_N) $ of outer automorphisms
of a free group of rank $ N $ is superrigid from the point of view of measure equivalence: any …

Abstract Ishan, Peterson and Ruth introduced the notion of von Neumann equivalence as a
non-commutative analogue of measure equivalence. They showed approximation …

We introduce a new equivalence relation on groups, which we call von Neumann
equivalence, that is coarser than both measure equivalence and W*-equivalence. We …

Von Neumann algebras are algebras of bounded operators on a Hilbert space that are
closed under taking the adjoint and in the weak operator topology. If their center consists …