Contact structures on principal circle bundles

Details Contact structures on principal circle bundles Contact structures on principal circle bundles

2011-07-25

arxiv.org/abs/1107.4948v2

Mathematics

Symplectic Geometry

14 pages, 1 figure; v2: changes to exposition, Sections 5.2, 5.3 and 6 are new

Scientific paper

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.

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