- Experiment. Math.
- Volume 9, Issue 3 (2000), 435-455.
Symplectic packings in cotangent bundles of tori
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.
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
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