Experimental Mathematics

Symplectic packings in cotangent bundles of tori

F. Miller Maley, Jean Mastrangeli, and Lisa Traynor


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.

Article information

Experiment. Math., Volume 9, Issue 3 (2000), 435-455.

First available in Project Euclid: 18 February 2003

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 57R17: Symplectic and contact topology

symplectic packings symplectic capacities lagrangian intersections linear programming Seshadri constants


Maley, F. Miller; Mastrangeli, Jean; Traynor, Lisa. Symplectic packings in cotangent bundles of tori. Experiment. Math. 9 (2000), no. 3, 435--455. https://projecteuclid.org/euclid.em/1045604678

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