Journal of Modern Dynamics (JMD)

Contact homology of orbit complements and implied existence

Pages: 409 - 472, Issue 3, July 2011      doi:10.3934/jmd.2011.5.409

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Al Momin - Department of Mathematics, Purdue University, 150 N. University St. , West Lafayette, IN 47906, United States (email)

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 of Angenent in [1]).

Keywords:  Reeb vector field, periodic orbit, forcing, contact homology, link complement, holomorphic curves, intersection theory.
Mathematics Subject Classification:  Primary: 37J45; Secondary: 53D42.

Received: November 2010;      Revised: October 2011;      Available Online: November 2011.