Localization for nonabelian group actions
| dc.creator | Jeffrey, L. C. | |
| dc.creator | Kirwan, F. C. | |
| dc.date | 1993-07-06 | |
| dc.date | 1994-02-13 | |
| dc.date.accessioned | 2026-07-07T08:57:47Z | |
| dc.date.available | 2026-07-07T08:57:47Z | |
| dc.description | Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group $K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $μ: X \to {\rm Lie}(K)^*$ and Marsden-Weinstein reduction $\xred = μ^{-1}(0)/K$. There is then a natural surjective map $κ_0$ from the equivariant cohomology $H^*_K(X) $ of $X$ to the cohomology $H^*(\xred)$. In this paper we prove a formula (Theorem 8.1, the residue formula) for the evaluation on the fundamental class of $\xred$ of any $η_0 \in H^*(\xred)$ whose degree is the dimension of $\xred$, provided that $0$ is a regular value of the moment map $μ$ on $X$. This formula is given in terms of any class $η\in H^*_K(X)$ for which $κ_0(η) = η_0$, and involves the restriction of $η$ to $K$-orbits $KF$ of components $F \subset X$ of the fixed point set of a chosen maximal torus $T \subset K$. Since $κ_0$ is | |
| dc.description | 42 pages, LaTex version no. 2.09, Introduction and Section 8 have been rewritten in revised version | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9307001 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9307001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147068 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Localization for nonabelian group actions | |
| dc.type | text |