Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: April 21, 2009
MathSciNet review: 2515819
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57R17, 57N10, 57N13

Retrieve articles in all journals with MSC (2000): 57R17, 57N10, 57N13


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04721-7
PII: S 0002-9947(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.