English

The topology of symplectic circle bundles

Geometric Topology 2011-05-19 v1 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.0711.2928,
  title  = {The topology of symplectic circle bundles},
  author = {Jonathan Bowden},
  journal= {arXiv preprint arXiv:0711.2928},
  year   = {2011}
}