SYMPLECTIC PACKINGS IN COTANGENT BUNDLES OF TORI

F. MILLER MALEY, JEAN MASTRANGELI, AND LISA TRAYNOR

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 ℤ^{n} and the embeddings induce isomorphisms of first homology. When the target and domains are 𝕋^{n} × V and 𝕋^{n} × 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, ℤ) 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.