Kirwan map and moduli space of flat connections

2003/06/24 by Racaniere, Sebastien
#22E67 #53D20 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0306341

Abstract

If K is a compact Lie group and g≥ 2 an integer, the space K^2g is endowed with the structure of a Hamiltonian space with a Lie group valued moment map Φ. Let β be in the centre of K. The reduction Φ^-1(β)/K is homeomorphic to a moduli space of flat connections. When K is simply connected, a direct consequence of a recent paper of Bott, Tolman and Weitsman is to give a set of generators for the K-equivariant cohomology of Φ^-1(β). Another method to construct classes in H^*_K(Φ^-1(β)) is by using the so called universal bundle. When the group is \Sun and β is a generator of the centre, these last classes are known to also generate the equivariant cohomology of Φ^-1(β). The aim of this paper is to compare the classes constructed using the result of Bott, Tolman and Weitsman and the ones using the universal bundle.

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