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arXiv · 1107.4948

Contact structures on principal circle bundles

Fan Ding·Hansjörg Geiges
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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.

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Fan Ding, Hansjörg Geiges. 2011-12-21. Contact structures on principal circle bundles. https://doi.org/10.1112/blms%2Fbds042

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