ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS

Ozawa showed in [21] that for any i.c.c, hyperbolic group, the associated group factor L Gamma 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 LP 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 >= 2, are virtually W*-superrigid.