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