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- W2510343240 abstract "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 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." @default.
- W2510343240 created "2016-09-16" @default.
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- W2510343240 date "2016-09-06" @default.
- W2510343240 modified "2023-09-27" @default.
- W2510343240 title "Unknotted Reeb orbits and nicely embedded holomorphic curves" @default.
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