Reeb flows without simple global surfaces of section [article]

Juno Kim, Yonghwan Kim, Otto van Koert
2022 arXiv   pre-print
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+ϵ-small perturbations of the Hamiltonian given on the symplectization.
arXiv:2104.03728v2 fatcat:476yuswos5d55hvdlaqmwjmwru