Bulletin of the London Mathematical Society



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FLAT CONNECTIONS ON ORIENTED 2-MANIFOLDS


LISA C. JEFFREY a1
a1 Department of Mathematics, University of Toronto, Toronto M5S 3G3, Canada jeffrey@math.toronto.edu

Article author query
jeffrey lc   [Google Scholar] 
 

Abstract

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)).

(Received October 10 2003)
(Revised April 27 2004)

Maths Classification

53D30 (primary); 14D20 (secondary).