Relations in the cohomology ring of the moduli space of flat

We consider the moduli space of flat SO(2n + 1)-connections (up to gauge transformations) on a Riemann surface, with fixed holonomy around a marked point. There are natural line bundles over this moduli space; we construct geometric representatives for the Chern classes of these line bundles, and prove that the ring generated by these Chern classes vanishes below the dimension of the moduli space, generalizing a conjecture of Newstead.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.