Reeb flows without simple global surfaces of section

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.

20 pages, 10 figures. Improved and corrected some arguments following suggestions of the referee. To appear in Involve

References in corpus (1)

• Surfaces of section for Seifert fibrations

Cited by in corpus (2)

• Bott-integrable Reeb flows on 3-manifolds
• From curve shortening to flat link stability and Birkhoff sections of geodesic flows