ScalingStacks

3.2.3 Moment map [03TV]

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3.2.3 Moment map

Consider a compact connected symplectic manifold (X,ω)(X,\omega) of dimension 2​n2n together with a Hamiltonian action of the torus TnT^{n}. Then one has an integrable system π:X→B0\pi:X\to B_{0}, where π\pi is the moment map of the action and B0=(L​i​e​(Tn))∗≃𝐑nB_{0}=(Lie(T^{n}))^{\ast}\simeq{{\bf R}}^{n}. Furthermore, it is well-known that B=π⁡(X)B=\pi(X) is a convex polytope and Bs​mB^{sm} is the interior of BB.

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