Surjectivity for Hamiltonian Loop Group Spacees
| dc.creator | Bott, Raoul | |
| dc.creator | Tolman, Susan | |
| dc.creator | Weitsman, Jonathan | |
| dc.date | 2002-10-02 | |
| dc.date.accessioned | 2026-07-07T04:51:27Z | |
| dc.date.available | 2026-07-07T04:51:27Z | |
| dc.description | 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 $μ: X \to L\fg^*$ is proper. We consider the function $|μ|^2: X \to \R$, and use a version of Morse theory to show that the inclusion map $j:μ^{-1}(0)\to X$ induces a surjection $j^*:H_G^*(X) \to H_G^*(μ^{-1}(0))$, 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. | |
| dc.identifier | https://arxiv.org/abs/math/0210036 | |
| dc.identifier | http://arxiv.org/abs/math/0210036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65154 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 53D20,22E67 | |
| dc.title | Surjectivity for Hamiltonian Loop Group Spacees | |
| dc.type | text |