English

A Reeb flow on the three-sphere without a disk-like global surface of section

Symplectic Geometry 2019-02-05 v1 Dynamical Systems

Abstract

We show that there are Reeb flows on the standard, tight three-sphere that do not admit global surfaces of section with one boundary component. In particular, the Reeb flows that we construct do not admit disk-like global surfaces of section. These Reeb flows are constructed using integrable systems, and a connected sum construction that extends the integrable system.

Cite

@article{arxiv.1902.01172,
  title  = {A Reeb flow on the three-sphere without a disk-like global surface of section},
  author = {Otto van Koert},
  journal= {arXiv preprint arXiv:1902.01172},
  year   = {2019}
}

Comments

10 pages, 5 figures

R2 v1 2026-06-23T07:31:22.835Z