The topology of symplectic circle bundles
Abstract
We consider circle bundles over compact threemanifolds with symplectic total spaces. We show that the base of such a space must be irreducible or the product of the twosphere 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2928
 Bibcode:
 2007arXiv0711.2928B
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry
 EPrint:
 Trans. Amer. Math. Soc. 361 (2009), no. 10, 54575468