Symplectic Forms on Moduli Spaces of Flat Connections on 2-manifolds

Details Symplectic Forms on Moduli Spaces of Flat Connections on 2-manifolds Symplectic Forms on Moduli Spaces of Flat Connections on 2-manifolds

1994-04-28

arxiv.org/abs/alg-geom/9404013v2

Proc. Georgia Intl. Topology Conference (Athens, GA, 1993), W. Kazez, ed., AMS/IP Studies in Advanced Mathematics 2 (1997) (Pa

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTex version 2.09 This paper will appear in Proceedings of the Georgia International Topology Conference (Athens, G

Scientific paper

Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group $\pi$ of a 2-manifold $\Sigma$ (the smooth analogues of ${\rm Hom} (\pi_1(\Sigma), G)/G$) and on relative character varieties of fundamental groups of 2-manifolds. We extend this construction to exhibit a symplectic form on the extended moduli space [J1] (a Hamiltonian $G$-space from which these moduli spaces may be obtained by symplectic reduction), and compute the moment map for the action of $G$ on the extended moduli space.

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