On real moduli spaces of holomorphic bundles over M-curves

Let F be a genus g curve and σ : F → F a real structure with the maximal possible number of fixed circles. We study the real moduli space N ′ = Fix ( σ # ) where σ # : N → N is the induced real structure on the moduli space N of stable holomorphic bundles of rank 2 over F with fixed non-trivial determinant. In particular, we calculate H ⁎ ( N ′ , Z ) in the case of g = 2 , generalizing Thaddeusʹ approach to computing H ⁎ ( N , Z ) .