Global surfaces of section for Reeb flows in dimension three and beyond

2017/12/05 by Umberto L. Hryniewicz, Hryniewicz, Umberto L., Pedro A. S. Salomão +1
Mathematics · #37Jxx #53Dxx #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1712.01925

openalex publication_date 2017/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic inequalities. Applications to topology and celestial mechanics are also presented.

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