THE HOMOLOGY OF MODULI SPACES ON A RIEMANN SURFACE AS A REPRESENTATION OF THE MAPPING CLASS GROUP

Abstract

Let $M_{g,k}$ be the moduli space of flat SU(2)-connections on a compact Riemann surface $\Sigma_g$ of genus $g \ge 2$ punctured in a point $p$ in a small open disc $D$, with holonomy $(-1)^k$ about $\partial D$. This paper gives an explicit decomposition of the rational intersection homology of $M_{g,k}$ into irreducible representations of the oriented mapping class group $\mbox{Map}^+(\Sigma_g)$ of $\Sigma_g$.

1991 Mathematics Subject Classification: primary 14D20; secondary 14H60, 55N33.