Intersection cohomology of representation spaces of surface groups

2001/01/31 by Young‐Hoon Kiem, Young-Hoon Kiem, Kiem, Young-Hoon
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG

paper · pdf · doi:10.48550/arxiv.math/0101256

arxiv created 2001/01/31 · openalex publication_date 2001/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space Hom(π₁(Σ),G)/G for a simply connected compact Lie group G is naturally embedded into the G equivariant cohomology of Hom(π₁(Σ),G) where Σ 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.

Citations

• The cosupport axiom, equivariant cohomology and the intersection cohomology of certain symplectic quotients

Related

• Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations
• Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface
• Intersection cohomology of rank two character varieties of surface groups
• Intersection cohomology of S¹ symplectic quotients and small resolutions
• Connected Components of The Space of Surface Group Representations