Copyright © The Author 2008. Published by Oxford University Press.
Maximal Ball Packings of Symplectic-Toric Manifolds
1 Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge MA 02139-4307, USA
2 University of Chicago, Department of Mathematics, 5734 South University Avenue, Chicago, Illinois 60637, USA
Correspondence: Correspondence to be sent to: apelayo{at}math.mit.edu
Let (M, 
, 
) be a symplectic-toric manifold of dimension at least four. This article investigates the symplectic ball packing problem in the toral equivariant setting. We show that the set of toric symplectic ball packings of M admits the structure of a convex polytope.
Previous work of the first author shows that up to equivalence, only (
1)2 and 2 admit density one packings when n = 2 and only n admits density one packings when n > 2. In contrast, we show that for a fixed n 
2 and each 
(0, 1), there are uncountably many genuinely inequivalent 2n-dimensional symplectic-toric manifolds with a maximal toric packing of density . This result follows from a general analysis of how the densities of maximal packings change while varying a given symplectic-toric manifold through a family of symplectic-toric manifolds that are equivariantly diffeomorphic but not equivariantly symplectomorphic.