Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

The topology of symplectic circle bundles

Author(s): Jonathan Bowden
Journal: Trans. Amer. Math. Soc. 361 (2009), 5457-5468.
MSC (2000): Primary 57R17; Secondary 57N10, 57N13
Posted: April 21, 2009
MathSciNet review: 2515819
Retrieve article in: PDF

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Abstract: 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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