Contact Homology of Orbit Complements and Implied Existence
Symplectic Geometry
2015-03-17 v2 Dynamical Systems
Abstract
For Reeb vector fields on closed 3-manifolds, cylindrical contact homology is used to show that the existence of a set of closed Reeb orbit with certain knotting/linking properties implies the existence of other Reeb orbits with other knotting/linking properties relative to the original set. We work out a few examples on the 3-sphere to illustrate the theory, and describe an application to closed geodesics on (a version of a result due to Angenent).
Keywords
Cite
@article{arxiv.1012.1386,
title = {Contact Homology of Orbit Complements and Implied Existence},
author = {Al Momin},
journal= {arXiv preprint arXiv:1012.1386},
year = {2015}
}
Comments
Section 5 was removed, as well as any assertions in the main theorems which depend on it. Changes to introduction, several typos corrected