Von Neumann Algebras of Sofic Groups with ${\beta }_1^{(2)}=0$ are Strongly $1$-Bounded

D. Shlyakhtenko

We show that if $\Gamma$ is an infinite finitely generated finitely presented sofic group with zero first $L^2$ Betti number then the von Neumann algebra $L(\Gamma )$ is strongly $1$-bounde…