Nombres de Betti $L^2$ et facteurs de type ${\rm II}

Nombres de Betti

L^{2}

et facteurs de type

{II}_{1}

[

L^{2}

Betti numbers and applications of the

p

-adic cohomology type II

_{1}

factors ]

Connes, Alain

Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Talk no. 920, p. 321-333

Abstract
Résumé

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.

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.

Zbl 1133.46032 | 1 citation in Numdam

Classification: 46L35, 57R30
Keywords:

L^{2}

Betti numbers, foliation, type II

_{1}

factor, fundamental group of a type II

_{1}

factor

@incollection{SB_2002-2003__45__321_0,
     author = {Connes, Alain},
     title = {Nombres de Betti $L^2$ et facteurs de type ${\rm II}\_1$},
     booktitle = {S\'eminaire Bourbaki : volume 2002/2003, expos\'es 909-923},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Association des amis de Nicolas Bourbaki, Soci\'et\'e math\'ematique de France},
     address = {Paris},
     number = {294},
     year = {2004},
     note = {talk:920},
     pages = {321-333},
     zbl = {1133.46032},
     language = {fr},
     url = {http://www.numdam.org/item/SB_2002-2003__45__321_0}
}

Connes, Alain. Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$, in Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Talk no. 920, pp. 321-333. http://www.numdam.org/item/SB_2002-2003__45__321_0/

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