MODULI SPACES OF FLAT SU(2)-BUNDLES OVER NON-ORIENTABLE SURFACES

We study the topology of the moduli space of flat SU(2)-bundles over a non-orientable surface Σ. This moduli space may be identified with the space of homomorphisms Hom (π1(Σ), SU(2)) modulo conjugation by SU(2). In particular, we compute the (rational) equivariant cohomology ring of Hom (π1(Σ), SU(2)) and use this to compute the ordinary cohomology groups of the quotient Hom (π1(Σ), SU(2))/SU(2). A key property is that the conjugation action is equivariantly formal.