The topology of symplectic circle bundles

Jonathan Bowden

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11 Citations (Scopus)

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 languageEnglish
Pages (from-to)5457-5468
Number of pages12
JournalTransactions of the American Mathematical Society
Volume361
Issue number10
DOIs
Publication statusPublished - Oct 2009
Externally publishedYes

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