Surjectivity for Hamiltonian Loop Group Spaces
نویسندگان
چکیده
Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,ω) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,ω), and assume that the moment map μ : X −→ Lg∗ is proper. We consider the function |μ|2 : X −→ R, and use a version of Morse theory to show that the inclusion map j : μ(0) −→ X induces a surjection j∗ : H∗ G(X) −→ H∗ G(μ−1(0)), in analogy with Kirwan’s surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces.
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