Intersection cohomology of representation spaces of surface groups

Details Intersection cohomology of representation spaces of surface groups Intersection cohomology of representation spaces of surface groups

2001-01-31

arxiv.org/abs/math/0101256v1

Mathematics

Algebraic Geometry

Scientific paper

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$ equivariant cohomology of $Hom(\pi_1(\Sigma),G)$ where $\Sigma$ is a closed Riemann surface. This enables us to compute the intersection cohomology as a graded vector space with intersection pairing, in terms of the equivariant cohomology ring. The case where $G=SU(2)$ -- the moduli space of rank 2 holomorphic vector bundles of even degree -- is discussed in detail.

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