2002/10/02 by Raoul Bott, Bott, Raoul, Susan Tolman +3
Mathematics · #22E67 #53D20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:22E67 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0210036
arxiv created 2002/10/02 · openalex publication_date 2002/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 → L\fg^* 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^*:HG^*(X) → HG^*(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.