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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 (π 1 (Σ), SU(2)) modulo conjugation by SU(2). In particular, we compute the (rational) equivariant cohomology ring of Hom (π 1 (Σ), SU(2)) and use this to compute the ordinary cohomology groups of the quotient Hom (π 1 (Σ), SU(2))/SU(2). A key property is that the conjugation action is equivariantly formal.

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