Poisson structures on certain moduli spaces for bundles on a surface
| dc.creator | Huebschmann, Johannes | |
| dc.date | 1994-11-23 | |
| dc.date.accessioned | 2026-07-07T09:12:27Z | |
| dc.date.available | 2026-07-07T09:12:27Z | |
| dc.description | Let $Σ$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $ξ\colon P \to Σ$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(ξ)$ of central Yang- Mills connections, for appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a diffeomorphism from $N(ξ)$ onto a certain representation space $\roman{Rep}_ξ(Γ,G)$, with reference to suitable smooth structures $C^{\infty}(N(ξ))$ and $C^{\infty}(\roman{Rep}_ξ(Γ,G))$ where $Γ$ denotes the universal central extension of the fundamental group of $Σ$. Given an invariant symmetric bilinear form on $g^*$, we construct here Poisson structures on $C^{\infty}(N(ξ))$ and $C^{\infty}(\roman{Rep}_ξ(Γ,G))$ in such a way that the mentioned diffeomorphism identifies them. When the form on $g^*$ is non-degenerate the Poisson structures are compatible with the stratifications where $\roman{Rep}_ξ(Γ,G)$ is endowed with the corresponding stratification and, furthermore, yield structures of a {\it stratified symplectic space\/}, preserved by the induced action of the mapping class group of $Σ$. | |
| dc.description | 22 pages, AMSTeX 2.1 | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9411009 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9411009 | |
| dc.identifier | Ann. Inst. Fourier 45 (1995) 65-91 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152028 | |
| dc.subject | Differential Geometry | |
| dc.title | Poisson structures on certain moduli spaces for bundles on a surface | |
| dc.type | text |