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

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.

Classification:  46L35,  57R30
Keywords: L 2 Betti numbers, foliation, type II 1 factor, fundamental group of a type II 1 factor
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     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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