Английская Википедия:Delzant's theorem

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In mathematics, a Delzant polytope is a convex polytope in <math>\mathbb{R}^n</math> such for each vertex <math>v</math>, exactly <math>n</math> edges meet at <math>v</math>, and these edges form a collection of vectors that form a <math>\mathbb{Z}</math>-basis of <math>\mathbb{Z}^n</math>. Delzant's theorem, introduced by Шаблон:Harvs, classifies effective Hamiltonian torus actions on compact connected symplectic manifolds by the image of the associated moment map, which is a Delzant polytope.

The theorem states that there is a bijective correspondence between symplectic toric manifolds (up to torus-equivariant symplectomorphism) and Delzant polytopes -- more precisely, the moment polytope of a symplectic toric manifold is a Delzant polytope, every Delzant polytope is the moment polytope of such a manifold, and any two such manifolds with the equivalent moment polytopes (up to translations) admit a torus-equivariant symplectomorphism between them.

References

• Шаблон:Citation

Шаблон:Differential-geometry-stub