Symplectic and Poisson structures of certain moduli spaces
| dc.creator | Huebschmann, Johannes | |
| dc.date | 1993-12-14 | |
| dc.date.accessioned | 2026-07-07T09:14:11Z | |
| dc.date.available | 2026-07-07T09:14:11Z | |
| dc.description | Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $π$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction due to A. Weinstein relying on techniques from equivariant cohomology may be refined so as to yield (i) a symplectic structure on a certain smooth manifold $\Cal M(\Cal P,G)$ containing the space $\roman{Hom}(π,G)$ of homomorphisms and, furthermore, (ii) a hamiltonian $G$-action on $\Cal M(\Cal P,G)$ preserving the symplectic structure, with momentum mapping $μ\colon \Cal M(\Cal P,G) \to g^*$, in such a way that the reduced space equals the space $\roman{Rep}(π,G)$ of representations. Our approach is somewhat more general in that it also applies to twisted moduli spaces; in particular, it yields the {\smc Narasimhan-Seshadri} moduli spaces of semistable holomorphic vector bundles by {\it symplectic reduction in finite dimensions}.This implies that, when the group $G$ is compact, such a twisted moduli space inherits a structure of {\it stratified symplectic space}, and that the strata of these twisted moduli spaces have finite symplectic volume. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9312112 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9312112 | |
| dc.identifier | Duke Math.J. 80 (1995) 737-756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152583 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Symplectic Geometry | |
| dc.title | Symplectic and Poisson structures of certain moduli spaces | |
| dc.type | text |