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June 2013 Packing numbers of rational ruled four-manifolds
Olguta Buse, Martin Pinsonnault
J. Symplectic Geom. 11(2): 269-316 (June 2013).

Abstract

We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic four-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit values for when an ellipsoid of type $E(a, b)$, with $\frac{b}{a} \in \mathbb{N}$, embeds in a polydisc $P(s,t)$. Under this integrality assumption, we also give an alternative proof of a recent result of M. Hutchings showing that the embedded contact homology capacities give sharp inequalities for embedding ellipsoids into polydisks.

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Olguta Buse. Martin Pinsonnault. "Packing numbers of rational ruled four-manifolds." J. Symplectic Geom. 11 (2) 269 - 316, June 2013.

Information

Published: June 2013
First available in Project Euclid: 11 November 2013

zbMATH: 1302.53093
MathSciNet: MR3046492

Rights: Copyright © 2013 International Press of Boston

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Vol.11 • No. 2 • June 2013
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