Amenable absorption in von Neumann algebras of hyperbolic groups

Adriana Fernandez I Quero

Using ultrapower analysis of von Neumann algebras along with methods in acylindrically hyperbolic groups we show the von Neumann algebra L(G) associated with any hyperbolic group G satisfies the following amenable absorption property: any infinite maximal amenable subgroup K in H and any amenable von Neumann subalgebra Q inside L(G) that has diffuse intersection with L(K) must satisfy that Q is contained in L(H). This strengthens a prior result of Boutonnet-Carderi. Similar, additional amenable absorption results are obtained when G is a mapping class group or a limit group in the sense of Sela.

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