A non-locally trivial $\mathrm{W}^*$-bundle with fixed factorial fibres

Kiefer Mommaerts

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arXiv · 2606.12134

A non-locally trivial $\mathrm{W}^*$-bundle with fixed factorial fibres

Kiefer Mommaerts

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Abstract

In this paper we construct the first example of a non-locally trivial $\mathrm{W}^*$-bundle whose fibres are all isomorphic to some fixed $\mathrm{II}_1$ factor. This is achieved by introducing a notion of uniformly having spectral gap for $\mathrm{W}^*$-bundles. For bundles with fixed factorial fibres, the negation of having this uniform spectral gap property provides an obstruction for being locally trivial. This results in seemingly elementary examples of $\mathrm{W}^*$-bundles whose fibres are all isomorphic to some fixed factor but that are not locally trivial, even over spaces with covering dimension equal to zero.

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BibTeX RIS

Kiefer Mommaerts. 2026-06-10. A non-locally trivial $\mathrm{W}^*$-bundle with fixed factorial fibres. https://arxiv.org/abs/2606.12134

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