Geometry of the intersection ring of the moduli space of flat connections and the conjectures of Newstead and Witten

Abstract

We develop geometric techniques to study the intersection ring of the moduli space  g ( t 1, …, t n ) of flat connections on a two-manifold Σ g of genus g with n marked points p 1, …, p n . We find explicit homology cycles dual to generators of this ring, which allow us to prove recursion relations in g and n for their intersection numbers. The recursion relations in the genus g are related to generalizations of the Newstead Conjecture and of some recursion relations due to Donaldson. The recursion relations in the number n of marked points yield analogs of the recursion relations appearing in the work of Witten and Kontsevich on moduli spaces of punctured curves.