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arXiv · 2212.00991

Special Hamiltonian $S^1$-actions on symplectic 4-manifolds

Mei-Lin Yau
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Abstract

In this paper we consider symplectic 4-manifolds $(M,\omega)$ with $c_1(M,\omega)=0$ which admit a Hamiltonian $S^1$-action together with an equivariant Maslov condition on orbits of the group action. We call such spaces {\em special Hamiltonian $S^1$-spaces}. It turns out that there are no compact special Hamiltonian $S^1$-spaces. We classify all exact special Hamiltonian $S^1$-spaces and show that all of them admit the structure of a Stein surface.

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Mei-Lin Yau. 2022-12-02. Special Hamiltonian $S^1$-actions on symplectic 4-manifolds. https://arxiv.org/abs/2212.00991

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