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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Cohomology and $L^2$-Betti numbers for subfactors
and quasi-regular inclusions - Dima Shlyakhtenko (
University of California\, Los Angeles)
DTSTART;TZID=Europe/London:20170125T113000
DTEND;TZID=Europe/London:20170125T123000
UID:TALK70271AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70271
DESCRIPTION: Co-authors: Sorin Popa (UCLA) and&n
bsp\;Stefaan Vaes (Leuven)
We intr
oduce \;L$^2$-Betti numbers\, as well as a gen
eral homology and cohomology theory for the standa
rd invariants of subfactors\, through the associat
ed quasi-regular symmetric enveloping inclusion of
II$_1$ factors. We actually develop a (co)homolog
y theory for arbitrary quasi-regular inclusions of
von Neumann algebras. For crossed products by cou
ntable groups \;&Gamma\;\, we recover the ordi
nary (co)homology of \;&Gamma\;. For Cartan su
balgebras\, we recover Gaboriau'\;s \;L$^2$
-Betti numbers for the associated equivalence rela
tion. In this common framework\, we prove that the
 \;L$^2$-Betti numbers vanish for amenable inc
lusions and we give cohomological characterization
s of property (T)\, the Haagerup property and amen
ability. We compute the \;L$^2$-Betti numbers
for the standard invariants of the Temperley-Lieb-
Jones subfactors and of the Fuss-Catalan subfactor
s\, as well as for free products and tensor produc
ts.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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