How to recognise a 4-ball when you see one

• Published in 2011
• Added on 2012-05-19

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.

Links

• http://arxiv.org/abs/1104.1543
• http://arxiv.org/pdf/1104.1543v3

Other information

BibTeX entry

@article{Geiges2011,
	key = {Geiges2011},
	type = {article},
	title = {How to recognise a 4-ball when you see one},
	author = {Geiges, Hansj{\"{o}}rg and Zehmisch, Kai},
	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.},
	comment = {},
	date_added = {2012-05-19},
	date_published = {2011-04-01},
	urls = {http://arxiv.org/abs/1104.1543,http://arxiv.org/pdf/1104.1543v3},
	collections = {Attention-grabbing titles,Geometry},
	month = {apr},
	pages = 26,
	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}
}