On spectral gap rigidity and Connes invariant $\chi (M)$
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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 $\chi (M)=1$.References
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Additional Information
- Sorin Popa
- Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
- MR Author ID: 141080
- Email: popa@math.ucla.edu
- 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
- © Copyright 2010 American Mathematical Society
- 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
- MathSciNet review: 2661553