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

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 use this to answer a question he posed in 1975, on the structure of McDuff factors $M$ with $\chi (M)=1$.

8 pages