Conference on noncommutative geometry / Conférence de géométrie non commutative

Collection Conference on noncommutative geometry / Conférence de géométrie non commutative

Organizer(s) Debord, Claire ; Le Gall, Pierre-Yves ; Tu, Jean-Louis ; Vaes, Stefaan ; Vassout, Stéphane ; Vergnioux, Roland

Date(s) 02/11/2015 - 06/11/2015

linked URL http://conferences.cirm-math.fr/1206.html

00:00:00 / 00:00:00

1 5

Chapters

Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions

By Stefaan Vaes

I present a joint work with S. Popa and D. Shlyakhtenko introducing a cohomology theory for quasi-regular inclusions of von Neumann algebras. In particular, we define $L^2$-cohomology and $L^2$-Betti numbers for such inclusions. Applying this to the symmetric enveloping inclusion of a finite index subfactor, we get a cohomology theory and a definition of $L^2$-Betti numbers for finite index subfactors, as well as for arbitrary rigid $C^²$-tensor categories. For the inclusion of a Cartan subalgebra in a $II_1$ factor, we recover Gaboriau’s $L^2$-Betti numbers for equivalence relations.

Information about the video

Date of recording 03/11/2015
Date of publication 02/12/2015
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18879303
Cite this video Vaes, Stefaan (03/11/2015). Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18879303
URL https://dx.doi.org/10.24350/CIRM.V.18879303

Domain(s)

Bibliography

Popa, S., Shlyakhtenko, D., Vaes, S. (2015). Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions. <arXiv:1511.07329> - http://arxiv.org/abs/1511.07329

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