Open Access
November 2005 Non-negative pinching, moduli spaces and bundles with infinitely many souls
Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann
J. Differential Geom. 71(3): 365-383 (November 2005). DOI: 10.4310/jdg/1143571988


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.


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Vitali Kapovitch. Anton Petrunin. Wilderich Tuschmann. "Non-negative pinching, moduli spaces and bundles with infinitely many souls." J. Differential Geom. 71 (3) 365 - 383, November 2005.


Published: November 2005
First available in Project Euclid: 28 March 2006

zbMATH: 1102.53020
MathSciNet: MR2198806
Digital Object Identifier: 10.4310/jdg/1143571988

Rights: Copyright © 2005 Lehigh University

Vol.71 • No. 3 • November 2005
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