Abstract
We show that if Γ is a finitely generated finitely presented sofic group with zero first L2-Betti number, then the von Neumann algebra L(Γ) is strongly 1-bounded in the sense of Jung. In particular, L(Γ)≆L(Λ) if Λ is any group with free entropy dimension >1, for example a free group. The key technical result is a short proof of an estimate of Jung
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