The action of the Torelli group on the homology of representation spaces is nontrivial

The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space RSU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace RSU(2)(M))irred of irreducibles. In this paper we compute the cohomology H∗ (RSU(2)(M)), H∗ (RSU(2)(M)irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.