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Reeb flows without simple global surfaces of section
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Reeb flows without simple global surfaces of section
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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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