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.
Original language | English |
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Pages (from-to) | 5457-5468 |
Number of pages | 12 |
Journal | Transactions of the American Mathematical Society |
Volume | 361 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2009 |
Externally published | Yes |