L 2 Betti numbers and applications of the p -adic cohomology type II 1 factors

Alain Connes

Séminaire Bourbaki (2002-2003)

  • Volume: 45, page 321-334
  • ISSN: 0303-1179

Abstract

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Damien Gaboriau showed recently that the L 2 Betti numbers of measured foliations with contractile leaves are invariants of the associated equivalence relation. Sorin Popa used this result, together with rigidity properties of type II 1 factors whose fundamental group is trivial.

How to cite

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Connes, Alain. "Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$." Séminaire Bourbaki 45 (2002-2003): 321-334. <http://eudml.org/doc/252141>.

@article{Connes2002-2003,
abstract = {Damien Gaboriau a montré récemment que les nombres de Betti $L^2$ des feuilletages mesurés à feuilles contractiles sont des invariants de la relation d’équivalence associée. Sorin Popa a utilisé ce résultat joint à des propriétés de rigidité des facteurs de type II$\{\}_1$ pour en déduire l’existence de facteurs de type II$\{\}_1$ dont le groupe fondamental est trivial.},
author = {Connes, Alain},
journal = {Séminaire Bourbaki},
keywords = {$L^2$ Betti numbers; foliation; type II$\{\}_1$ factor; fundamental group of a type II$\{\}_1$ factor},
language = {fre},
pages = {321-334},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Nombres de Betti $L^2$ et facteurs de type $\{\rm II\}_1$},
url = {http://eudml.org/doc/252141},
volume = {45},
year = {2002-2003},
}

TY - JOUR
AU - Connes, Alain
TI - Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$
JO - Séminaire Bourbaki
PY - 2002-2003
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 45
SP - 321
EP - 334
AB - Damien Gaboriau a montré récemment que les nombres de Betti $L^2$ des feuilletages mesurés à feuilles contractiles sont des invariants de la relation d’équivalence associée. Sorin Popa a utilisé ce résultat joint à des propriétés de rigidité des facteurs de type II${}_1$ pour en déduire l’existence de facteurs de type II${}_1$ dont le groupe fondamental est trivial.
LA - fre
KW - $L^2$ Betti numbers; foliation; type II${}_1$ factor; fundamental group of a type II${}_1$ factor
UR - http://eudml.org/doc/252141
ER -

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