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Annales scientifiques de l'ENS - Parutions - série 4, 46 (2013)

Parutions < série 4, 46

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 46, fascicule 1 (2013)

Ionut Chifan, Thomas Sinclair
On the structural theory of II_1 factors of negatively curved groups
Annales scientifiques de l'ENS 46, fascicule 1 (2013), 1-33

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Résumé :
Sur la structure des facteurs de type II_1 associé avec les groupes de courbure négative
Ozawa a montré dans [22] que, pour un groupe c.c.i. hyperbolique, le facteur de type II_1 associé est solide. En devéloppant une nouvelle approche, qui combine les méthodes de Peterson [30], d'Ozawa et Popa [], et d'Ozawa [26], nous renforçons ce résultat en montrant que ce facteur est fortement solide. En combinant nos méthodes avec un résultat d'Ioana de superrigidité des cocycles [13], nous prouvons que les actions des réseaux de Sp(n,1), n2, sont virtuellement W^*-superrigides.

Mots-clefs : Forte solidité, groupes de courbure négative, groupes <>

Abstract:
Ozawa showed in [22] that for any i.c.c.hyperbolic group, the associated group factor L is solid. Developing a new approach that combines some methods of Peterson [30], Ozawa and Popa [], and Ozawa [26], we strengthen this result by showing that L is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [13], we show that profinite actions of lattices in Sp(n,1), n2, are virtually W^*-superrigid.

Keywords: Strong solidity, negatively curved groups, bi-exact groups

Class. math. : 46L10; 20F67


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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