Group systems, groupoids, and moduli spaces of parabolic bundles

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dc.creatorGuruprasad, K.
dc.creatorHuebschmann, J.
dc.creatorJeffrey, L.
dc.creatorWeinstein, A.
dc.date1995-10-23
dc.date.accessioned2026-07-07T09:12:37Z
dc.date.available2026-07-07T09:12:37Z
dc.descriptionLet $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $π$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of conjugacy classes in $G$, one for each puncture. A finite-dimensional construction used earlier to obtain a symplectic structure on the moduli space of flat $G$-bundles over compact $M$ is extended to the punctured case. It yields a symplectic structure on a certain smooth manifold $\Cal M_{\bold C}$ containing the space $\roman{Hom}(π,G)_{\bold C}$ of homomorphisms mapping the generators corresponding to the punctures into the corresponding conjugacy classes. It also yields a Hamiltonian $G$-action on $\Cal M_{\bold C}$ such that the reduced space equals the moduli space $\roman{Rep}(π,G)_{\bold C}$ of representations. For $G$ compact, each such space, obtained by finite-dimensional symplectic reduction, is a {\it stratified symplectic space\/}. For $G=U(n)$ one gets moduli spaces of semistable holomorphic parabolic bundles or spaces closely related to them.
dc.descriptionAMSTeX 2.1, 33 pages
dc.identifierhttps://arxiv.org/abs/dg-ga/9510006
dc.identifierhttp://arxiv.org/abs/dg-ga/9510006
dc.identifierDuke Math. J. 89 (1997), 377-412
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152078
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.titleGroup systems, groupoids, and moduli spaces of parabolic bundles
dc.typetext

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