Contact homology of orbit complements and implied existence

Al Momin

doi:10.3934/jmd.2011.5.409

Article Contents

2011, Volume 5, Issue 3: 409-472. Doi: 10.3934/jmd.2011.5.409

This issue Previous Article Next Article Outer billiards on the Penrose kite: Compactification and renormalization

Contact homology of orbit complements and implied existence

Al Momin^1,

1.
Department of Mathematics, Purdue University, 150 N. University St. , West Lafayette, IN 47906

Received: November 2010

Revised: October 2011

Published: November 2011

Abstract / Introduction Related Papers Cited by

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]).

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Mathematics Subject Classification: Primary: 37J45; Secondary: 53D42.

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