Abstract
We summarize recent work ([W],[JW91a], [JW92]) on the symplectic geometry of the moduli space of flat connections on a two-manifold. This work is based on the existence in these moduli spaces of Hamiltonian torus actions. Using these torus actions and the images of the corresponding moment maps we find a simple description of the moduli spaces, and show how it can be used to compute symplectic volumes and other quantities arising in the geometry and topology of the moduli space.
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Supported in part by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291
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Jeffrey, L.C., Weitsman, J. (1993). Torus Actions, Moment Maps, and the Symplectic Geometry of the Moduli Space of Flat Connections on a Two-Manifold. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_28
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DOI: https://doi.org/10.1007/978-1-4899-1612-9_28
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