Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
Reeb flows without simple global surfaces of section

### Juno Kim, Yonghwan Kim and Otto van Koert

Vol. 15 (2022), No. 5, 813–842
##### 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. Moreover, we prove that this property is stable with respect to ${C}^{4+𝜖}$-small perturbations of the Hamiltonian given on the symplectization.

##### Keywords
global surfaces of section, integrable Reeb flows, Hamiltonian dynamics
##### Mathematical Subject Classification
Primary: 37J55, 53D10