Nonnegative pinching, moduli spaces and bundles with infinitely many souls

Abstract

We show that in each dimension $n\ge 10$ there exist infinite sequences of homotopy equivalent but mutually non-homeomorphic closed simply connected Riemannian $n$-manifolds with $0\le \sec \le 1$, positive Ricci curvature and uniformly bounded diameter. We also construct open manifolds of fixed diffeomorphism type which admit infinitely many complete nonnegatively pinched metrics with souls of bounded diameter such that the souls are mutually non-homeomorphic. Finally, we construct examples of noncompact manifolds whose moduli spaces of complete metrics with $\sec \ge 0$ have infinitely many connected components.

Cited by in corpus (6)

• Examples of Riemannian Manifolds with non-negative sectional curvature
• Nonconnected Moduli Spaces of Nonnegative Sectional Curvature Metrics on Simply Connected Manifolds
• On the topology of moduli spaces of non-negatively curved Riemannian metrics
• Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$
• Non-negative versus positive scalar curvature
• Open manifolds with non-homeomorphic positively curved souls