Moduli spaces of Ricci positive metrics in dimension five

We use the similar to invariants of spinc Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many nondiffeomorphic five-dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal S1 bundles over #(CP2)-C-a #(b) CP2 and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5-manifolds with fundamental group Z(2) admitting free S-1 actions with simply connected quotients.