On spectral gap rigidity and Connes invariant $χ(M)$

Details On spectral gap rigidity and Connes invariant $χ(M)$ On spectral gap rigidity and Connes invariant $χ(M)$

2009-09-30

arxiv.org/abs/0909.5639v2

Mathematics

Operator Algebras

8 pages

Scientific paper

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 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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