Amenable Absorption in von Neumann Algebras of Hyperbolic Groups (cont.)

Professor Ionut Chifan

Abstract: We prove that the von Neumann algebra L(G) associated with any hyperbolic group (G) satisfies the following amenable absorption property: for any infinite maximal amenable subgroup H \leq G and any amenable von Neumann subalgebra Q \subset L(G) with diffuse intersection with L(H), one must have Q \subset L(H). This strengthens a result of Boutonnet and Carderi [BC13]. We also establish similar amenable absorption results for the broader class of acylindrically hyperbolic groups, including relatively hyperbolic groups, mapping class groups, and limit groups. This is based on a recent joint work with Juan Felipe Ariza Mejìa, Adriana Fernandez Quero, and Adrian Ioana.

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