Nombres de Betti L 2 et facteurs de type II 1
Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Exposé no. 920, pp. 321-333.

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.

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.

Classification : 46L35, 57R30
Mot clés : nombres de Betti $L^2$, feuilletage, facteur de type II${}_1$, groupe fondamental d’un facteur de type II${}_1$
Keywords: $L^2$ Betti numbers, foliation, type II${}_1$ factor, fundamental group of a type II${}_1$ factor
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Connes, Alain. Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$, dans Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Exposé no. 920, pp. 321-333. http://www.numdam.org/item/SB_2002-2003__45__321_0/

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