%0 Journal Article
%T Contact Homology of Orbit Complements and Implied Existence
%A Al Momin
%J Mathematics
%D 2010
%I arXiv
%R 10.3934/jmd.2011.5.409
%X 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).
%U http://arxiv.org/abs/1012.1386v2