Reeb flows without simple global surfaces of section
Symplectic Geometry
2023-03-08 v2
Abstract
We construct, for any given positive integer , Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than 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 -small perturbations of the Hamiltonian given on the symplectization.
Cite
@article{arxiv.2104.03728,
title = {Reeb flows without simple global surfaces of section},
author = {Juno Kim and Yonghwan Kim and Otto van Koert},
journal= {arXiv preprint arXiv:2104.03728},
year = {2023}
}
Comments
20 pages, 10 figures. Improved and corrected some arguments following suggestions of the referee. To appear in Involve