局部平凡W*-Bundles
Locally Trivial W*-Bundles
摘要：
我们证明了一个tracially连续的W $^*$ -丛$\mathcal{M}$在一个紧凑的T2空间$X$与所有纤维同构的超有限II $_1$ -因子$\mathcal{R}$是局部平凡的已经是全球平凡的。证明使用了Popa和Takesaki所证明的自同构群$\mathrm{Aut}({\mathcal{R}})$的可压缩性。对$X$的覆盖维数没有限制。
英文摘要：
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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