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BIRS Workshop Lecture Videos

von Neumann algebras of certain groups with vanishing first Betti number Shlyakhtenko, Dimitri


We show that the von Neumann algebra of a finitely generated finitely presented sofic group is strongly 1-bounded in the sense of Jung. As a corollary we obtain that such a von Neumann algebra cannot be written as a non-trivial free product and in particular cannot be a free group factor.

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