An effective algorithm for the cohomology ring of symplectic reductions
| dc.creator | Goldin, R. F. | |
| dc.date | 2001-10-01 | |
| dc.date | 2002-05-07 | |
| dc.date.accessioned | 2026-07-07T04:43:36Z | |
| dc.date.available | 2026-07-07T04:43:36Z | |
| dc.description | Let G be a compact torus acting on a compact symplectic manifold M in a Hamiltonian fashion, and T a subtorus of G. We prove that the kernel of $κ:H_G^*(M)\to H^*(M//G)$ is generated by a small number of classes $α\in H_G^*(M)$ satisfying very explicit restriction properties. Our main tool is the equivariant Kirwan map, a natural map from the G-equivariant cohomology of M to the G/T-equivariant cohomology of the symplectic reduction of M by T. We show this map is surjective. This is an equivariant version of the well-known result that the (nonequivariant) Kirwan map $κ:H_G^*(M)\to H^*(M//G)$ is surjective. We also compute the kernel of the equivariant Kirwan map, generalizing the result due to Tolman and Weitsman in the case T=G and allowing us to apply their methods inductively. This result is new even in the case that dim T = 1. We close with a worked example: the cohomology ring of the product of two $\C P^2$s, quotiented by the diagonal 2-torus action. | |
| dc.description | 16 pages, 4 figures, to appear in Geometric and Functional Analysis | |
| dc.identifier | https://arxiv.org/abs/math/0110022 | |
| dc.identifier | http://arxiv.org/abs/math/0110022 | |
| dc.identifier | Geom. Func. Anal., Vol. 12 (2002) 567-583 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62298 | |
| dc.subject | Symplectic Geometry | |
| dc.title | An effective algorithm for the cohomology ring of symplectic reductions | |
| dc.type | text |