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

• Published in 2011
In the collections
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.

## Other information

pages
26

### BibTeX entry

@article{Geiges2011,
abstract = {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.},
author = {Geiges, Hansj{\"{o}}rg and Zehmisch, Kai},
month = {apr},
pages = 26,
title = {How to recognise a 4-ball when you see one},
url = {http://arxiv.org/abs/1104.1543 http://arxiv.org/pdf/1104.1543v3},
year = 2011,
archivePrefix = {arXiv},
eprint = {1104.1543},
primaryClass = {math.SG},
urldate = {2012-05-19},
collections = {Attention-grabbing titles,Geometry}
}