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Bibliographic Metadata

  • Title
    How to recognize a 4-ball when you see one
  • Author
    Geiges, Hansjörg ; Zehmisch, Kai
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 525-554
  • Published
    2013
  • Language
    English
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-55309457138 
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Abstract
  • 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.
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