Abstract: Let \Sigma be a compact connected oriented 2-manifold of genus g , and let p be a point on \Sigma. We define a space S_g(t) consisting of certain irreducible representations of the fundamental group of \Sigma - { p } , modulo conjugation by SU(N).
This space has interpretations in algebraic geometry, gauge theory and topological quantum field theory; in particular if \Sigma has a Kahler structure then S_g(t) is the moduli space of parabolic vector bundles of rank N over \Sigma. We construct tautological line bundles on S_g(t) and prove that the ring generated by their Chern classes vanishes above a certain degree. This is joint work with Jonathan Weitsman.