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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On spectral gap rigidity and Connes invariant $ \chi (M)$


Author: Sorin Popa
Journal: Proc. Amer. Math. Soc. 138 (2010), 3531-3539
MSC (2000): Primary 46L10, 46L37, 46L40
Published electronically: June 15, 2010
MathSciNet review: 2661553
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Abstract: We calculate Connes' invariant $ \chi (M)$ for certain II$ _{1}$ factors $ M$ that can be obtained as inductive limits of subfactors with spectral gap. Then we use this to answer a question he posed in 1975 on the structure of McDuff factors $ M$ with $ \chi (M)=1$.


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Additional Information

Sorin Popa
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
Email: popa@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10277-0
PII: S 0002-9939(2010)10277-0
Received by editor(s): September 30, 2009
Received by editor(s) in revised form: October 25, 2009, and October 31, 2009
Published electronically: June 15, 2010
Additional Notes: This work was supported in part by NSF Grant 0601082
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society