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The topology of symplectic circle bundles


Author: Jonathan Bowden
Journal: Trans. Amer. Math. Soc. 361 (2009), 5457-5468
MSC (2000): Primary 57R17; Secondary 57N10, 57N13
DOI: https://doi.org/10.1090/S0002-9947-09-04721-7
Published electronically: April 21, 2009
MathSciNet review: 2515819
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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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Additional Information

Jonathan Bowden
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München, Germany
Email: jonathan.bowden@mathematik.uni-muenchen.de

DOI: https://doi.org/10.1090/S0002-9947-09-04721-7
Received by editor(s): November 19, 2007
Published electronically: April 21, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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