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Nombres de Betti L 2 et facteurs de type II 1

Alain Connes (2002/2003)

Séminaire Bourbaki

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.

Notes on tiled incompressible tori

Leonid Plachta (2012)

Open Mathematics

Let Θ denote the class of essential tori in a closed braid complement which admit a standard tiling in the sense of Birman and Menasco [Birman J.S., Menasco W.W., Special positions for essential tori in link complements, Topology, 1994, 33(3), 525–556]. Moreover, let R denote the class of thin tiled tori in the sense of Ng [Ng K.Y., Essential tori in link complements, J. Knot Theory Ramifications, 1998, 7(2), 205–216]. We define the subclass B ⊂ Θ of typical tiled tori and show that R ⊂ B. We also...

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