Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
Symplectic Geometry
2020-01-08 v2 Dynamical Systems
Abstract
We prove that every nondegenerate contact form on a closed connected three-manifold, such that the associated contact structure has torsion first Chern class, has either two or infinitely many simple Reeb orbits. By previous results it follows that under the above assumptions, there are infinitely many simple Reeb orbits if the three-manifold is not the three-sphere or a lens space. We also show that for non-torsion contact structures, every nondegenerate contact form has at least four simple Reeb orbits.
Keywords
Cite
@article{arxiv.1701.02262,
title = {Torsion contact forms in three dimensions have two or infinitely many Reeb orbits},
author = {Dan Cristofaro-Gardiner and Michael Hutchings and Dan Pomerleano},
journal= {arXiv preprint arXiv:1701.02262},
year = {2020}
}
Comments
42 pages, minor corrections and expository improvements