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A dynamical characterization of universally tight lens spaces. (English) Zbl 1418.37089

Summary: 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 non-degenerate Reeb flows on \((L(p,q),\xi _{\text{std}})\) with prescribed binding orbits.

MSC:

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37J55 Contact systems
53D35 Global theory of symplectic and contact manifolds
53D10 Contact manifolds (general theory)
57R17 Symplectic and contact topology in high or arbitrary dimension
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