Unknotted Reeb orbits and nicely embedded holomorphic curves
| Autor: | Cioba, Alexandru, Wendl, Chris |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We exhibit a distinctly low-dimensional dynamical obstruction to the existence of Liouville cobordisms: for any contact 3-manifold admitting an exact symplectic cobordism to the tight 3-sphere, every nondegenerate contact form admits an embedded Reeb orbit that is unknotted and has self-linking number -1. The same is true moreover for any contact structure on a closed 3-manifold that is reducible. Our results generalize an earlier theorem of Hofer-Wysocki-Zehnder for the 3-sphere, but use somewhat newer techniques: the main idea is to exploit the intersection theory of punctured holomorphic curves in order to understand the compactification of the space of so-called "nicely embedded" curves in symplectic cobordisms. In the process, we prove a local adjunction formula for holomorphic annuli breaking along a Reeb orbit, which may be of independent interest. Comment: 50 pages, 5 figures; v3 implements minor changes suggested by the referees; to appear in J. Symplectic Geom |
| Databáze: | arXiv |
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