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The
Weinstein conjecture for stable Hamiltonian structures
Michael Hutchings and Clifford Henry Taubes |
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Geometry & Topology 13 (2009) 901–941
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Abstract |
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We use the equivalence between embedded contact homology and Seiberg–Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let be a closed oriented connected –manifold with a stable Hamiltonian structure, and let denote the associated Reeb vector field on . We prove that if is not a –bundle over , then has a closed orbit. Along the way we prove that if is a closed oriented connected –manifold with a contact form such that all Reeb orbits are nondegenerate and elliptic, then is a lens space. Related arguments show that if is a closed oriented –manifold with a contact form such that all Reeb orbits are nondegenerate, and if is not a lens space, then there exist at least three distinct embedded Reeb orbits. |
Keywords
dynamical system, Seiberg–Witten, Floer homology
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Mathematical Subject Classification 2000
Primary: 57R17, 57R57, 53D40
Secondary: 57R58
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References |
Publication
Received: 21 September 2008
Revised: 8 December 2008
Accepted: 20 November 2008
Published: 8 January 2200
Proposed: Yasha Eliashberg
Seconded: Peter Ozsvath, Leonid Polterovich
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Authors |
| Michael Hutchings | |
| Mathematics Department 970 Evans Hall University of California Berkeley, CA 94720 USA |
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| Clifford Henry Taubes | |
| Mathematics Department Harvard University Cambridge, MA 02138 USA |
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