Locally Trivial W*-Bundles

Abstract

We prove that a tracially continuous W${}^{\ast }$-bundle $\mathcal{M}$ over a compact Hausdorff space $X$ with all fibres isomorphic to the hyperfinite II${}_1$-factor $\mathcal{R}$ that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group $\mathrm{Aut}(\mathcal{R})$ shown by Popa and Takesaki. There is no restriction on the covering dimension of $X$.

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

References in corpus (1)

• Nuclear dimension and Z-stability