Examples of manifolds of positive Ricci curvature (Q1096190)

This paper presents some new examples of simply connected Riemannian manifolds with positive Ricci curvature, which admit no metric with nonnegative sectional curvature, in both compact and noncompact cases. Specifically, these examples show that there is not an upper bound on the total Betti number for manifolds with positive Ricci curvature in a fixed dimension, and a manifold with positive Ricci curvature can be of infinite topological type if it is non-compact. They thus settle a long standing problem in Riemannian geometry.