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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01275 |
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Table of Contents:
- We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that symplecticity is equivalent to factor-compatibility. We also classify them up to diffeomorphism. Finally, we construct a symplectic four-dimensional small cover whose orbit polytope is not combinatorially equivalent to a product of two polygons.