On the structural theory of ${\rm II}_1$ factors of negatively curved groups

Chifan, Ionut; Sinclair, Thomas

doi:10.24033/asens.2183

On the structural theory of

{II}_{1}

factors of negatively curved groups
[Sur la structure des facteurs de type

{II}_{1}

associé avec les groupes de courbure négative]

Chifan, Ionut ; Sinclair, Thomas

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 46 (2013) no. 1, pp. 1-33

Abstract (VO)
Résumé

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.

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 $Sp (n, 1)$ , $n \geq 2$ , sont virtuellement $W^{*}$ -superrigides.

EuDML MR Zbl | 1 citation dans Numdam

DOI : 10.24033/asens.2183

Classification : 46L10, 20F67
Keywords: strong solidity, negatively curved groups, bi-exact groups
Mots-clés : Forte solidité, groupes de courbure négative, groupes «bi-exacts»

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     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},
     pages = {1--33},
     year = {2013},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
     number = {1},
     doi = {10.24033/asens.2183},
     mrnumber = {3087388},
     zbl = {1290.46053},
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     url = {https://www.numdam.org/articles/10.24033/asens.2183/}
}

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Chifan, Ionut; Sinclair, Thomas. On the structural theory of ${\rm II}_1$ factors of negatively curved groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 46 (2013) no. 1, pp. 1-33. doi: 10.24033/asens.2183

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