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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm139, 24 pages, doi:10.1093/imrn/rnm139 published on February 5, 2008
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Copyright © The Author 2008. Published by Oxford University Press.

Maximal Ball Packings of Symplectic-Toric Manifolds

Alvaro Pelayo1, and Benjamin Schmidt2

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, {sigma}, {psi}) 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 (CP1)2 and CP2 admit density one packings when n = 2 and only CPn admits density one packings when n > 2. In contrast, we show that for a fixed n ≥ 2 and each {delta} isin (0, 1), there are uncountably many genuinely inequivalent 2n-dimensional symplectic-toric manifolds with a maximal toric packing of density {delta}. 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.

Communicated by Prof. Yasha Eliashberg



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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
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Right arrow Articles by Schmidt, B.
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