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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
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Abstract |
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We construct, for any given positive integer , Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than 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 -small perturbations of the Hamiltonian given on the symplectization. |
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Keywords
global surfaces of section, integrable Reeb flows,
Hamiltonian dynamics
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Mathematical Subject Classification
Primary: 37J55, 53D10
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Milestones
Received: 1 September 2021
Accepted: 4 February 2022
Published: 3 March 2023
Communicated by Colin Adams
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Authors |
| Juno Kim | |
| Department of Statistics Seoul National University Seoul South Korea |
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| Yonghwan Kim | |
| Department of Mathematical
Sciences Seoul National University Seoul South Korea |
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| Otto van Koert | |
| Department of Mathematical
Sciences Seoul National University Seoul South Korea |
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