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

Ionut Chifan; Thomas Sinclair

Annales scientifiques de l'École Normale Supérieure (2013)

  • Volume: 46, Issue: 1, page 1-33
  • ISSN: 0012-9593

Abstract

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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 ≥ 2 , are virtually W * -superrigid.

How to cite

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Chifan, Ionut, and Sinclair, Thomas. "On the structural theory of ${\rm II}_1$ factors of negatively curved groups." Annales scientifiques de l'École Normale Supérieure 46.1 (2013): 1-33. <http://eudml.org/doc/272124>.

@article{Chifan2013,
abstract = {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 $L\Gamma $ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in $\{\rm Sp\}(n,1)$, $n\ge 2$, are virtually $W^*$-superrigid.},
author = {Chifan, Ionut, Sinclair, Thomas},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {strong solidity; negatively curved groups; bi-exact groups},
language = {eng},
number = {1},
pages = {1-33},
publisher = {Société mathématique de France},
title = {On the structural theory of $\{\rm II\}_1$ factors of negatively curved groups},
url = {http://eudml.org/doc/272124},
volume = {46},
year = {2013},
}

TY - JOUR
AU - Chifan, Ionut
AU - Sinclair, Thomas
TI - On the structural theory of ${\rm II}_1$ factors of negatively curved groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2013
PB - Société mathématique de France
VL - 46
IS - 1
SP - 1
EP - 33
AB - 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 $L\Gamma $ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in ${\rm Sp}(n,1)$, $n\ge 2$, are virtually $W^*$-superrigid.
LA - eng
KW - strong solidity; negatively curved groups; bi-exact groups
UR - http://eudml.org/doc/272124
ER -

References

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