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arXiv · 2605.01275

Symplectic small covers in dimension four

Suyoung Choi
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Abstract

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.

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Suyoung Choi. 2026-05-02. Symplectic small covers in dimension four. https://arxiv.org/abs/2605.01275

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