English

Reeb flows without simple global surfaces of section

Symplectic Geometry 2023-03-08 v2

Abstract

We construct, for any given positive integer nn, Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than nn 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 C4+ϵC^{4+\epsilon}-small perturbations of the Hamiltonian given on the symplectization.

Keywords

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

R2 v1 2026-06-24T00:57:44.722Z