Symplectic small covers in dimension four
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915978564075520 |
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| author | Choi, Suyoung |
| author_facet | Choi, Suyoung |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01275 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symplectic small covers in dimension four Choi, Suyoung Symplectic Geometry Primary 57S12, Secondary 53D05, 57K43, 52B11 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. |
| title | Symplectic small covers in dimension four |
| topic | Symplectic Geometry Primary 57S12, Secondary 53D05, 57K43, 52B11 |
| url | https://arxiv.org/abs/2605.01275 |