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Maximal symplectic packings in ${\mathbb {P}^2}$

Part of: Symplectic geometry, contact geometry Differential topology

Published online by Cambridge University Press:  01 November 2007

Emmanuel Opshtein
Emmanuel Opshtein*
Affiliation:
IRMA, 7 rue René Descartes, 67084 Strasbourg cedex, France (email: opshtein@math.u-strasbg.fr)
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Abstract

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In this paper we describe the intersections between the balls of maximal symplectic packings of $\mathbb {P}^2$. This analysis shows the existence of singular points for maximal packings of $\mathbb {P}^2$ by more than three equal balls. It also yields a construction of a class of very regular examples of maximal packings by five balls.

Keywords

symplectic topologysymplectic packings

MSC classification

Secondary: 53D05: Symplectic manifolds, general 57R17: Symplectic and contact topology

Information

Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1558 - 1575
Copyright
Copyright © Foundation Compositio Mathematica 2007

References

This research was supported by The Israel Science Foundation (Grant No. 1227/06).