Inventiones mathematicae

, Volume 155, Issue 2, pp 225–251 | Cite as

Surjectivity for Hamiltonian loop group spaces

Article

Abstract

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:XL\(\mathfrak{g}\)* is proper. We consider the function |μ|2:X→ℝ, and use a version of Morse theory to show that the inclusion map j-1(0)→X induces a surjection j*:HG*(X)→HG*-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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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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