A dynamical characterization of universally tight lens spaces

2013/06/30 by Umberto L. Hryniewicz, Joan E. Licata, Pedro A. S. Salomão · 1 citation
Mathematics · #math.SG #math.DS #math.GT #msc:53D10

paper · pdf · doi:10.1112/plms/pdu043

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

arxiv created 2014/07/12 · arxiv updated 2017/05/17

Abstract

We give necessary and sufficient conditions for a closed connected co-orientable contact 3-manifold (M,ξ) 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),ξ_{\rm std}) with prescribed binding orbits.

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