English

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

Operator Algebras 2009-10-13 v2

Abstract

We calculate Connes' invariant χ(M)\chi(M) for certain II1_1 factors MM 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 MM with χ(M)=1\chi(M)=1.

Cite

@article{arxiv.0909.5639,
  title  = {On spectral gap rigidity and Connes invariant $\chi(M)$},
  author = {Sorin Popa},
  journal= {arXiv preprint arXiv:0909.5639},
  year   = {2009}
}

Comments

8 pages

R2 v1 2026-06-21T13:52:31.648Z