Surjectivity for Hamiltonian loop group spaces |
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Authors: | Raoul Bott Susan Tolman and Jonathan Weitsman |
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Institution: | (1) Department of Mathematics, Harvard University, 02138 Cambridge, MA, USA;(2) Department of Mathematics, University of Illinois at Urbana-Champaign, 61801 Urbana, IL, USA;(3) Department of Mathematics, University of California, 95064 Santa Cruz, CA, USA |
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Abstract: | Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,), and assume that the moment map :XL
* is proper. We consider the function ||2:X, and use a version of Morse theory to show that the inclusion map j:-1(0)X induces a surjection j
*:H
G
*(X)H
G
*(-1(0)), in analogy with Kirwans 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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Keywords: | |
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