Damien Gaboriau a montré récemment que les nombres de Betti 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 pour en déduire l’existence de facteurs de type II dont le groupe fondamental est trivial.
Damien Gaboriau showed recently that the 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 factors whose fundamental group is trivial.
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
@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}, series = {Ast\'erisque}, note = {talk:920}, pages = {321--333}, publisher = {Association des amis de Nicolas Bourbaki, Soci\'et\'e math\'ematique de France}, address = {Paris}, number = {294}, year = {2004}, zbl = {1133.46032}, language = {fr}, url = {http://www.numdam.org/item/SB_2002-2003__45__321_0/} }
TY - CHAP AU - Connes, Alain TI - Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$ BT - Séminaire Bourbaki : volume 2002/2003, exposés 909-923 AU - Collectif T3 - Astérisque N1 - talk:920 PY - 2004 SP - 321 EP - 333 IS - 294 PB - Association des amis de Nicolas Bourbaki, Société mathématique de France PP - Paris UR - http://www.numdam.org/item/SB_2002-2003__45__321_0/ LA - fr ID - SB_2002-2003__45__321_0 ER -
%0 Book Section %A Connes, Alain %T Nombres de Betti $L^2$ et facteurs de type ${\rm II}_1$ %B Séminaire Bourbaki : volume 2002/2003, exposés 909-923 %A Collectif %S Astérisque %Z talk:920 %D 2004 %P 321-333 %N 294 %I Association des amis de Nicolas Bourbaki, Société mathématique de France %C Paris %U http://www.numdam.org/item/SB_2002-2003__45__321_0/ %G fr %F SB_2002-2003__45__321_0
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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