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

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.

33 pages, 3 figures. This is an extended version of a paper written for Proceedings of the ICM, Rio 2018; in v3 we made minor additional corrections, updated references, added a reference to work of Lu on the Conley Conjecture

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• A dynamical characterization of universally tight lens spaces
• Morse theory, closed geodesics, and the homology of free loop spaces

Cited by in corpus (1)

• From curve shortening to flat link stability and Birkhoff sections of geodesic flows