Obstructions to Smooth Full-Holonomy Cayley Fibrations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917364876967936 |
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| author | Majewski, Viktor F. Rzemieniecki, Jacek |
| author_facet | Majewski, Viktor F. Rzemieniecki, Jacek |
| contents | We study smooth fibrations of compact torsion-free Spin(7)-manifolds by Cayley submanifolds. Using geometric and topological constraints coming from the Spin(7)-structure, we show that only two topological configurations can arise. One of these is excluded by a spinnability criterion for fiber bundles, with the relevant hypothesis verified using gauge-theoretic input, while the remaining case is reduced to an open conjecture in 4-manifold topology. In particular, this rules out smooth Cayley fibrations on all known examples of compact torsion-free Spin(7)-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26920 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Obstructions to Smooth Full-Holonomy Cayley Fibrations Majewski, Viktor F. Rzemieniecki, Jacek Differential Geometry We study smooth fibrations of compact torsion-free Spin(7)-manifolds by Cayley submanifolds. Using geometric and topological constraints coming from the Spin(7)-structure, we show that only two topological configurations can arise. One of these is excluded by a spinnability criterion for fiber bundles, with the relevant hypothesis verified using gauge-theoretic input, while the remaining case is reduced to an open conjecture in 4-manifold topology. In particular, this rules out smooth Cayley fibrations on all known examples of compact torsion-free Spin(7)-manifolds. |
| title | Obstructions to Smooth Full-Holonomy Cayley Fibrations |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.26920 |