On spectral gap rigidity and Connes invariant 𝜒(𝑀)

Popa, Sorin

doi:10.1090/S0002-9939-2010-10277-0

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
DOI: https://doi.org/10.1090/S0002-9939-2010-10277-0
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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