Toric symplectic ball packing
نویسنده
چکیده
We define and solve the toric version of the symplectic ball packing problem, in the sense of listing all 2n-dimensional symplectic–toric manifolds which admit a perfect packing by balls embedded in a symplectic and torus equivariant fashion. In order to do this we first describe a problem in geometric–combinatorics which is equivalent to the toric symplectic ball packing problem. Then we solve this problem using arguments from Convex Geometry and Delzant theory. Applications to symplectic blowing–up are also presented, and some further questions are raised in the last section.
منابع مشابه
Maximal ball packings of symplectic-toric manifolds
Let (M, σ, ψ) be a symplectic-toric manifold of dimension at least four. This paper 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 (CP)2 and CP admit density one packings when n = 2 and onl...
متن کاملTopology of Spaces of Equivariant Symplectic Embeddings
We compute the homotopy type of the space of Tn-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic–toric manifold (M, σ), and use this computation to define a Z≥0-valued step function on R≥0 which is an invariant of the symplectic–toric type of (M, σ). We conclude with a discussion of the partially equivariant case of th...
متن کاملNon-compact Symplectic Toric Manifolds
The paradigmatic result in symplectic toric geometry is the paper of Delzant that classifies compact connected symplectic manifolds with effective completely integrable torus actions, the so called (compact) symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the torus; its image is a simple unim...
متن کاملCategories of Symplectic Toric Manifolds as Picard Stack Torsors
We outline a proof that the stack of symplectic toric G-manifolds over a fixed orbit space W is a torsor for the stack of symplectic toric G-principal bundles over W .
متن کاملSymplectic Toric Orbifolds Eugene Lerman and Susan Tolman
A symplectic toric orbifold is a compact connected orbifold M , a symplectic form ω on M , and an effective Hamiltonian action of a torus T on M , where the dimension of T is half the dimension of M . We prove that there is a one-to-one correspondence between symplectic toric orbifolds and convex rational simple polytopes with positive integers attached to each facet.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008