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On the structural theory of ${II}_{1}$ factors of negatively curved groups

Ionut Chifan; Thomas Sinclair — 2013

Annales scientifiques de l'École Normale Supérieure

Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor $L Γ$ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that $L Γ$ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in $Sp (n, 1)$ , $n \geq 2$ , are virtually $W^{*}$ -superrigid.

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On the structural theory of II 1 factors of negatively curved groups

On the structural theory of ${II}_{1}$ factors of negatively curved groups