Contact Homology of Orbit Complements and Implied Existence

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 $S^2$ (a version of a result due to Angenent).

Section 5 was removed, as well as any assertions in the main theorems which depend on it. Changes to introduction, several typos corrected

References in corpus (4)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Knot Floer homology detects fibred knots
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Reeb vector fields and open book decompositions

Cited by in corpus (6)

• Cylindrical contact homology and topological entropy
• A Poincaré-Birkhoff theorem for tight Reeb flows on $S^3$
• The cylindrical contact homology of universally tight sutured contact solid tori
• Automatic transversality in contact homology I: Regularity
• Global surfaces of section for Reeb flows in dimension three and beyond
• Homological invariants of codimension 2 contact submanifolds