Contact structures on principal circle bundles
Symplectic Geometry
2014-02-26 v2 Differential Geometry
Abstract
We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an invariant contact structure, only provided the trivial bundle does. In particular, all circle bundles over 4-manifolds admit invariant contact structures. We also discuss the Bourgeois construction of contact structures on odd-dimensional tori in this context, and we relate our results to recent work of Massot, Niederkrueger and Wendl on weak symplectic fillings in higher dimensions.
Keywords
Cite
@article{arxiv.1107.4948,
title = {Contact structures on principal circle bundles},
author = {Fan Ding and Hansjörg Geiges},
journal= {arXiv preprint arXiv:1107.4948},
year = {2014}
}
Comments
14 pages, 1 figure; v2: changes to exposition, Sections 5.2, 5.3 and 6 are new