Curvature, diameter, and quotient manifolds

This paper gives improved counterexamples to a question by Grove ([11], 5.7). The question was whether for each positive integer n and real number D, the simply connected closed Riemannian n-manifolds M with sectional curvature -1 and diameter D fall into only finitely many rational homotopy types. This was suggested by Gromov's theorem which bounds the Betti numbers of M in terms of n and D It was known that there can be infinitely many integral homotopy types already in dimension 7, perhaps first by Aloff and Wallach