Abstract:We prove that the Natsume-Olsen non-commutative spheres $\mathbb{S}^{2n-1}_{\theta}$ dualize for rational deformation parameters to provide examples of quantum branched covers over their respective centers' maximal spectra, embeddable into locally trivial $C^*$ bundles precisely when said spheres are classical; this, despite the bundles in question being of finite type over dimensional strata. The proof of the noted rigidity phenomenon relies on the quantum analogue of the 3-sphere's Heegaard splitting as a pushout of two solid tori.
| Comments: | 9 pages + references |
| Subjects: | Quantum Algebra (math.QA); Algebraic Topology (math.AT); Functional Analysis (math.FA); Operator Algebras (math.OA) |
| MSC classes: | 46M20 55R10, 46L85, 46L65, 53B21, 46L30, 55R40, 55S40 |
| Cite as: | arXiv:2605.24007 [math.QA] |
| (or arXiv:2605.24007v1 [math.QA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24007 arXiv-issued DOI via DataCite |
From: Alexandru Chirvăsitu L. [view email]
[v1]
Tue, 19 May 2026 13:20:14 UTC (18 KB)
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