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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26920 |
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Table of 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.