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arXiv · 2104.03728

Reeb flows without simple global surfaces of section

Juno Kim·Yonghwan Kim·Otto van Koert
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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. We prove that this property is stable with respect to $C^{4+\epsilon}$-small perturbations of the Hamiltonian given on the symplectization.

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Juno Kim, Yonghwan Kim, Otto van Koert. 2021-04-08. Reeb flows without simple global surfaces of section. https://doi.org/10.2140/involve.2022.15.813

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