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Reeb flows without simple global surfaces of section

Juno Kim, Yonghwan Kim and Otto van Koert

Vol. 15 (2022), No. 5, 813–842
Abstract

We construct, for any given positive integer n, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than n boundary components. We use a connected sum operation for open books to construct such systems. Moreover, we prove that this property is stable with respect to C4+𝜖-small perturbations of the Hamiltonian given on the symplectization.

Keywords
global surfaces of section, integrable Reeb flows, Hamiltonian dynamics
Mathematical Subject Classification
Primary: 37J55, 53D10
Milestones
Received: 1 September 2021
Accepted: 4 February 2022
Published: 3 March 2023

Communicated by Colin Adams
Authors
Juno Kim
Department of Statistics
Seoul National University
Seoul
South Korea
Yonghwan Kim
Department of Mathematical Sciences
Seoul National University
Seoul
South Korea
Otto van Koert
Department of Mathematical Sciences
Seoul National University
Seoul
South Korea