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arXiv · 1601.05964

Locally Trivial W*-Bundles

Samuel Evington·Ulrich Pennig
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Abstract

We prove that a tracially continuous W$^*$-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 $X$.

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Samuel Evington, Ulrich Pennig. 2016-01-22. Locally Trivial W*-Bundles. https://doi.org/10.1142/s0129167x16500889

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