A dynamical characterization of universally tight lens spaces

Abstract

We give necessary and sufficient conditions for a closed connected co-orientable contact $3$-manifold $(M,\xi )$ to be a standard lens space based on assumptions on the Reeb flow associated to a defining contact form. Our methods also provide rational global surfaces of section for nondegenerate Reeb flows on $(L(p,q),{\xi }_{\mathrm{std}})$ with prescribed binding orbits.

60 pages, 3 figures. To appear in the Proceedings of the London Mathematical Society

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