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...

Verfasser: Geiges, Hansjörg
Zehmisch, Kai
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.