How to recognise a 4-ball when you see one

Details How to recognise a 4-ball when you see one How to recognise a 4-ball when you see one

2011-04-08

arxiv.org/abs/1104.1543v2

Mathematics

Symplectic Geometry

26 pages, 2 figures; v2: minor changes and corrections

Scientific paper

We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as a 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 non-squeezing, and the non-existence of exact Lagrangian surfaces in standard symplectic 4-space.

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