Surjectivity for Hamiltonian loop group spaces

Raoul Bott, Susan Tolman, Jonathan Weitsman

Research output: Contribution to journalArticlepeer-review


Let G be a compact Lie group, and let LG denote the corresponding loop group. Lei (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-1 (0) → X induces a surjection j* : H* G(X) → H*G-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.

Original languageEnglish (US)
Pages (from-to)225-251
Number of pages27
JournalInventiones Mathematicae
Issue number2
StatePublished - 2004

ASJC Scopus subject areas

  • Mathematics(all)


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