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2000 Symplectic packings in cotangent bundles of tori
F. Miller Maley, Jean Mastrangeli, Lisa Traynor
Experiment. Math. 9(3): 435-455 (2000).

Abstract

Finding optimal packings of a symplectic manifold with symplectic embeddings of balls is a well known problem. In the following, an alternate symplectic packing problem is explored where the target and domains are 2n-dimensional manifolds which have first homology group equal to $\funnyZ^n$ and the embeddings induce isomorphisms of first homology. When the target and domains are $\funnyT^n \times V$ and $\funnyT^n \times U$ in the cotangent bundle of the torus, all such symplectic packings give rise to packings of $V$ by copies of $U$ under $\GL(n,\funnyZ)$ and translations. For arbitrary dimensions, symplectic packing invariants are computed when packing a small number of objects. In dimensions 4 and 6, computer algorithms are used to calculate the invariants associated to packing a larger number of objects. These alternate and classic symplectic packing invariants have interesting similarities and differences.

Citation

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F. Miller Maley. Jean Mastrangeli. Lisa Traynor. "Symplectic packings in cotangent bundles of tori." Experiment. Math. 9 (3) 435 - 455, 2000.

Information

Published: 2000
First available in Project Euclid: 18 February 2003

zbMATH: 0972.52010
MathSciNet: MR1795876

Subjects:
Primary: 53D35
Secondary: 57R17

Keywords: lagrangian intersections , linear programming , Seshadri constants , symplectic capacities , symplectic packings

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 3 • 2000
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