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Torsion contact forms in
three dimensions have two or infinitely many Reeb orbits
Dan Cristofaro-Gardiner, Michael Hutchings and Daniel Pomerleano |
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Geometry & Topology 23 (2019) 3601–3645
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Abstract |
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We prove that every nondegenerate contact form on a closed connected three-manifold such that the associated contact structure has torsion first Chern class has either two or infinitely many simple Reeb orbits. By previous results it follows that under the above assumptions, there are infinitely many simple Reeb orbits if the three-manifold is not the three-sphere or a lens space. We also show that for nontorsion contact structures, every nondegenerate contact form has at least four simple Reeb orbits. |
Keywords
Reeb dynamics, Weinstein conjecture, embedded contact
homology
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Mathematical Subject Classification 2010
Primary: 53D10
Secondary: 53D42
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References |
Publication
Received: 21 June 2018
Accepted: 24 March 2019
Published: 30 December 2019
Proposed: Yasha Eliashberg
Seconded: Tomasz Mrowka, Leonid Polterovich
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Authors |
| Dan Cristofaro-Gardiner | |
| Mathematics Department University of California, Santa Cruz Santa Cruz, CA United States |
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| Michael Hutchings | |
| Mathematics Department University of California, Berkeley Berkeley, CA United States |
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| Daniel Pomerleano | |
| Mathematics Department University of Massachusetts, Boston Boston, MA United States |
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