Nombres de Betti $L^2$ et facteurs de type ${\mathrm{II}}_1$

Connes, Alain

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.

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