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Symplectic forms invariant under free circle actions on 4--manifolds

Boguslaw Hajduk·Rafal Walczak
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Abstract

Let $M^4$ be a smooth compact manifold with a free circle action generated by a vector field $X.$ Then for any invariant symplectic form $ω$ on $M$ the contracted form $ι_X ω$ is nondegenerate. Using the map $ω--> ι_X ω$ and the related map to $H^1(M / S^1, R)$ we study the topology of the space $S_{inv}$ of invariant symplectic forms. In particular we give a description of $π_0 S_{inv}(M^4)$ in terms of the unit Thurston ball.

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Boguslaw Hajduk, Rafal Walczak. 2003-12-26. Symplectic forms invariant under free circle actions on 4--manifolds. https://arxiv.org/abs/math/0312465

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