Manifolds of low cohomogeneity and positive Ricci curvature

We classify compact asystatic G-manifolds with fixed point singular orbits in cohomogeneity ⩽3 up to equivariant diffeomorphism. From this we derive existence results for invariant metrics of positive Ricci curvature on such objects. We also develop non-existence results for invariant metrics of positive Ricci curvature in cohomogeneity four.