Extra structure on the cohomology of configuration spaces of closed orientable surfaces

Abstract

The rational homology of unordered configuration spaces of points on any surface was studied by Drummond-Cole and Knudsen. We compute the rational cohomology of configuration spaces on a closed orientable surface, keeping track of the mixed Hodge numbers and the action of the symplectic group on the cohomology. We find a series with coefficients in the Grothendieck ring of sp(2g) that describes explicitly the decomposition of the cohomology into irreducible representations. From that we deduce the mixed Hodge numbers and the Betti numbers, obtaining a new formula without cancellations.

18 pages, exposition improved and added an example

References in corpus (6)

• Betti numbers of configuration spaces of surfaces
• A non-Levi branching rule in terms of Littelmann paths
• Splitting of the homology of the punctured mapping class group
• Computing cohomology of configuration spaces
• Betti numbers of unordered configuration spaces of the torus
• Asymptotic growth of Betti numbers of ordered configuration spaces on an elliptic curve