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arXiv · 1510.08670

Transversely holomorphic flows and contact circles on spherical 3-manifolds

Hansjörg Geiges·Jesús Gonzalo
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Abstract

Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint. We describe a complex analogue of the classical Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic monodromy of closed leaves. The Bott invariant allows us to formulate a generalised Gauß-Bonnet theorem. We compute these invariants for the Poincaré foliations on the 3-sphere and derive rigidity statements, including a uniformisation theorem for orbifolds. These results are then applied to the classification of taut contact circles.

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Hansjörg Geiges, Jesús Gonzalo. 2016-04-12. Transversely holomorphic flows and contact circles on spherical 3-manifolds. https://arxiv.org/abs/1510.08670

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