On the structural theory of  II 1 factors of negatively curved groups
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 1, p. 1-33

Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor LΓ 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 LΓ 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), n2, are virtually W * -superrigid.

Ozawa a montré dans [21] 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 [29], d’Ozawa et Popa [27, 28], et d’Ozawa [25], 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 [12], nous prouvons que les actions des réseaux de Sp (n,1), n2, sont virtuellement W * -superrigides.

DOI : https://doi.org/10.24033/asens.2183
Classification:  46L10,  20F67
Keywords: strong solidity, negatively curved groups, bi-exact groups
@article{ASENS_2013_4_46_1_1_0,
     author = {Chifan, Ionut and Sinclair, Thomas},
     title = {On the structural theory of~${\rm II}\_1$ factors of negatively curved groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
     number = {1},
     year = {2013},
     pages = {1-33},
     doi = {10.24033/asens.2183},
     zbl = {1290.46053},
     mrnumber = {3087388},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2013_4_46_1_1_0}
}
Chifan, Ionut; Sinclair, Thomas. On the structural theory of ${\rm II}_1$ factors of negatively curved groups. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 1, pp. 1-33. doi : 10.24033/asens.2183. http://www.numdam.org/item/ASENS_2013_4_46_1_1_0/

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