Groups and Operator Algebras Seminar
Speaker: Daniel Drimbe (KU Leuven)
Title: Measure equivalence rigidity via s-malleable deformations
Abstract: In this talk we provide a class of groups $\mathcal M$ for which the following unique prime factorization result holds: if $G_1, ... ,G_m\in\mathcal M$ and $G_1\times ... \times G_m$ is measure equivalent to a product $H_1\times ... \times H_n$ of icc groups, then $n\geq m$, and if $n=m$ then, after permutation of the indices, $G_i$ is measure equivalent to $H_i$, for all $1\leq i\leq n$. This provides an analogue of Monod and Shalom's theorem for groups that belong to $\mathcal M$. Class $\mathcal M$ is constructed using groups whose von Neumann algebras admit an s-malleable deformation in the sense of Sorin Popa and it contains all icc non-amenable groups $G$ for which either (i) $G$ is an arbitrary wreath product group with amenable base or (ii) $G$ admits an unbounded 1-cocycle into its left regular representation. Consequently, we derive several orbit equivalence rigidity results for actions of product groups that belong to $\mathcal M$.
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