Manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type

Abstract

We construct a complete n-dimensinal (n ≥ 6) Riemannian manifold of positive Ricci curvature with quadratically asymptotically nonnegative sectional curvature and infinite topological type. This gives a negative answer to a problem proposed by Jiping Sha and Zhongmin Shen [12] in the case of n ≥ 6.