Contact Homology of orbit complements and implied existence, preprint 2010

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 S2 (a version of a result of Angenent in [Ang05]). 1