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

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

2003-12-26

arxiv.org/abs/math/0312465v1

Mathematics

Symplectic Geometry

21 pages

Scientific paper

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 $\omega$ on $M$ the contracted form $\iota_X \omega$ is nondegenerate. Using the map $\omega --> \iota_X \omega$ 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 $\pi_0 S_{inv}(M^4)$ in terms of the unit Thurston ball.

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