A Reeb flow on the three-sphere without a disk-like global surface of\n section

2019/02/04 by Otto van Koert, van Koert, Otto
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1902.01172

openalex publication_date 2019/02/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We show that there are Reeb flows on the standard, tight three-sphere that do\nnot admit global surfaces of section with one boundary component. In\nparticular, the Reeb flows that we construct do not admit disk-like global\nsurfaces of section. These Reeb flows are constructed using integrable systems,\nand a connected sum construction that extends the integrable system.\n

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