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Ellipsoid embeddings and symplectic packing stability

Part of: Differential topology Symplectic geometry, contact geometry

Published online by Cambridge University Press:  04 March 2013

O. Buse  and
R. Hind
O. Buse
Affiliation:
IUPUI Department of Mathematical Sciences, 402 N. Blackford St., Indianapolis, IN 46202, USA email buse@math.iupui.edu
R. Hind
Affiliation:
University of Notre Dame, Department of Mathematics, 255 Hurley, Notre Dame, IN 46556, USA email Richard.K.Hind.1@nd.edu
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Abstract

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We prove packing stability for rational symplectic manifolds. This will rely on a general symplectic embedding result for ellipsoids which assumes only that there is no volume obstruction and that the domain is sufficiently thin relative to the target. We also obtain easily computable bounds for the Embedded Contact Homology capacities which are sufficient to imply the existence of some symplectic volume filling embeddings in dimension 4.

Keywords

symplectic embeddingsymplectic packingsymplectic ellipsoidsymplectic capacitiesEmbedded Contact Homology (ECH)

MSC classification

Secondary: 53D35: Global theory of symplectic and contact manifolds 57R17: Symplectic and contact topology
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 5 , May 2013 , pp. 889 - 902
Copyright
© The Author(s) 2013 

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