Symplectic Forms on Moduli Spaces of Flat Connections on 2manifolds
Abstract
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 2manifold $\Sigma$ (the smooth analogues of ${\rm Hom} (\pi_1(\Sigma), G)/G$) and on relative character varieties of fundamental groups of 2manifolds. 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.
 Publication:

arXiv eprints
 Pub Date:
 April 1994
 arXiv:
 arXiv:alggeom/9404013
 Bibcode:
 1994alg.geom..4013J
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory
 EPrint:
 12 pages, LaTex version 2.09 This paper will appear in Proceedings of the Georgia International Topology Conference (Athens, GA, August 1993), ed. W. Kazez (International Press). The present version (April 1996) is essentially the version that will appear in print. Several sign errors have been corrected. Some errors have been corrected in the proof of nondegeneracy of the symplectic form (Section 5) on an open dense set in the extended moduli space