Relations in the cohomology ring of the moduli space of flat $SO(2n+1)$-connections on a Riemann surface

摘要

We consider the moduli space of flat $SO(2n+1)$-connections (up to gaugetransformations) on a Riemann surface, with fixed holonomy around a markedpoint. There are natural line bundles over this moduli space; we constructgeometric representatives for the Chern classes of these line bundles, andprove that the ring generated by these Chern classes vanishes below thedimension of the moduli space, generalising a conjecture of Newstead.