Reeb flows without simple global surfaces of section

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 sta...

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Published in:arXiv.org 2022-07
Main Authors: Kim, Juno, Kim, Yonghwan, Otto van Koert
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Homology
Perturbation
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Otto van Koert
description 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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Perturbation
title Reeb flows without simple global surfaces of section
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