English

Locally Trivial W*-Bundles

Operator Algebras 2019-10-03 v2

Abstract

We prove that a tracially continuous W^*-bundle M\mathcal{M} over a compact Hausdorff space XX with all fibres isomorphic to the hyperfinite II1_1-factor R\mathcal{R} that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group Aut(R)\mathrm{Aut}({\mathcal{R}}) shown by Popa and Takesaki. There is no restriction on the covering dimension of XX.

Keywords

Cite

@article{arxiv.1601.05964,
  title  = {Locally Trivial W*-Bundles},
  author = {Samuel Evington and Ulrich Pennig},
  journal= {arXiv preprint arXiv:1601.05964},
  year   = {2019}
}

Comments

20 pages, this version will be published in the International Journal of Mathematics

R2 v1 2026-06-22T12:34:48.057Z