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Bulletin of the London Mathematical Society 2005 37(1):1-14; doi:10.1112/S002460930400373X
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© London Mathematical Society

Flat Connections on Oriented 2-Manifolds

Lisa C. Jeffrey

Department of Mathematics, University of Toronto Toronto M5S 3G3, Canada; jeffrey{at}math.toronto.edu

Received 10 October 2003. Revision received 27 April 2004.

This paper aims to provide a survey on the subject of representations of fundamental groups of 2-manifolds, or in other guises flat connections on orientable 2-manifolds or moduli spaces parametrizing holomorphic vector bundles on Riemann surfaces. It emphasizes the relationships between the different descriptions of these spaces. The final two sections of the paper outline results of the author and Kirwan on the cohomology rings of certain of the spaces described earlier (formulas for intersection numbers that were discovered by Witten (Commun. Math. Phys. 141 (1991) 153–209 and J. Geom. Phys. 9 (1992) 303–368) and given a mathematical proof by the author and Kirwan (Ann. of Math. 148 (1998) 109–196)). 2000 Mathematics Subject Classification 53D30 (primary), 14D20 (secondary).


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