Delzant's theorem

(that is, it is a simple polytope), and there are integer vectors parallel to these edges forming a

Delzant's theorem, introduced by Thomas Delzant (1988), 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.

transformations) admit a torus-equivariant symplectomorphism between them.

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