Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact discrete planar groups
| dc.creator | Huebschmann, Johannes | |
| dc.date | 1994-12-21 | |
| dc.date.accessioned | 2026-07-07T09:12:29Z | |
| dc.date.available | 2026-07-07T09:12:29Z | |
| dc.description | Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary infinite orientation preserving cocompact planar discrete group of euclidean or non-euclidean motions $π$ and yields (i) a symplectic structure on a certain smooth manifold $\Cal M$ containing the space $\roman{Hom}(π,G)$ of homomorphisms and, furthermore, (ii) a hamiltonian $G$-action on $\Cal M$ preserving the symplectic structure together with a momentum mapping in such a way that the reduced space equals the space $\roman{Rep}(π,G)$ of representations. More generally, the construction also applies to certain spaces of projective representations. For $G$ compact, the resulting spaces of representations inherit structures of {\it stratified symplectic space\/} in such a way that the strata have finite symplectic volume . For example, {\smc Mehta-Seshadri} moduli spaces of semistable holomorphic parabolic bundles with rational weights or spaces closely related to them arise in this way by {\it symplectic reduction in finite dimensions\/}. | |
| dc.description | AMSTeX 2.1, 14 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9412003 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9412003 | |
| dc.identifier | Duke Math. J. 80 (1995), 757-770 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152034 | |
| dc.subject | Differential Geometry | |
| dc.title | Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact discrete planar groups | |
| dc.type | text |