Manifolds of positive Ricci curvature, quadratically asymptotically nonnegative curvature, and infnite Betti numbers

In a previous paper, we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimension $ge 6$. The purpose of the present paper is to use a different way to exhibit a family of complete $I$-dimensinal ($Ige5$) Riemannian manifolds of positive Ricci curvature, quadratically asymptotically nonnegative sectional curvature, and certain infinite Betti number $b_j$ ($2le jle I-2$).