The geometry of the intersection ring of the moduli space of flat connections and the conjectures of Newstead and Witten
Northeastern University, U.S.A.
We show how the Chern ring of the moduli space of flat connections on a Riemann surface (equivalently, the moduli of vector bundles) can be described in terms of the intersections of geometric (not algebraic!) cycles. These intersections are easy to compute and give the vanishing of the Chern ring in high degree (the Newstead-Ramanan Conjecture) as we as recursion relations in genus and number of marked points which are remarkably similar to those appearing in the stable cohomology ring of the moduli of curves (Witten-Kontsevich).
Similar constructions can be made in the much simpler case of moduli spaces of polygons.