## Journal of Differential Geometry

### Non-negative pinching, moduli spaces and bundles with infinitely many souls

#### Abstract

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

#### Article information

Source
J. Differential Geom., Volume 71, Number 3 (2005), 365-383.

Dates
First available in Project Euclid: 28 March 2006

https://projecteuclid.org/euclid.jdg/1143571988

Digital Object Identifier
doi:10.4310/jdg/1143571988

Mathematical Reviews number (MathSciNet)
MR2198806

Zentralblatt MATH identifier
1102.53020

#### Citation

Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich. Non-negative pinching, moduli spaces and bundles with infinitely many souls. J. Differential Geom. 71 (2005), no. 3, 365--383. doi:10.4310/jdg/1143571988. https://projecteuclid.org/euclid.jdg/1143571988