The topology of symplectic circle bundles

Details The topology of symplectic circle bundles The topology of symplectic circle bundles

2007-11-19

arxiv.org/abs/0711.2928v1

Trans. Amer. Math. Soc. 361 (2009), no. 10, 5457--5468

Mathematics

Geometric Topology

Scientific paper

We consider circle bundles over compact three-manifolds with symplectic total spaces. We show that the base of such a space must be irreducible or the product of the two-sphere with the circle. We then deduce that such a bundle admits a symplectic form if and only if it admits one that is invariant under the circle action in three special cases: namely if the base is Seifert fibered, has vanishing Thurston norm, or if the total space admits a Lefschetz fibration.

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