How to recognize a 4-ball when you see one
We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as one convex boundary component. We establish the following dichotomy: either the cobordism is diffeomorphic to a ball, or there is a periodic Reeb orbit of quantifiably...
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Dokumenttypen: | Artikel |
Erscheinungsdatum: | 2013 |
Publikation in MIAMI: | 05.05.2014 |
Datum der letzten Änderung: | 27.07.2015 |
Quelle: | Münster Journal of Mathematics, 6 (2013), S. 525-554 |
Angaben zur Ausgabe: | [Electronic ed.] |
Fachgebiet (DDC): | 510: Mathematik |
Lizenz: | InC 1.0 |
Sprache: | English |
Format: | PDF-Dokument |
URN: | urn:nbn:de:hbz:6-55309457138 |
Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-55309457138 |
Onlinezugriff: | MJM_2013_6_525-554.pdf |
We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as one convex boundary component. We establish the following dichotomy: either the cobordism is diffeomorphic to a ball, or there is a periodic Reeb orbit of quantifiably short period in the concave boundary of the cobordism. This allows us to give a unified treatment of various results concerning Reeb dynamics on contact 3-manifolds, symplectic fillability, the topology of symplectic cobordisms, symplectic nonsqueezing, and the nonexistence of exact Lagrangian surfaces in standard symplectic 4-space.