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

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

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 celesti...

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Bibliographic Details
Main Authors: Hryniewicz, Umberto L, Salomão, Pedro A. S
Format: Journal Article
Language:English
Published: 05-12-2017
Subjects:
Mathematics - Differential Geometry
Mathematics - Dynamical Systems
Mathematics - Symplectic Geometry
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.1712.01925