The Topology of Open Manifolds with Nonnegative Ricci Curvature

Abstract

We survey all results concerning the topology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature that have no additional conditions other than restrictions to the dimension, volume growth or diameter growth of the manifold. We will also present relevant examples and list open problems.

arXiv commentsurvey article, 30 pages, 12 figures, (v2: change in the construction of the dyadic solenoid complement, other minor adjustments and typos corrected)

Cited by in corpus (8)

• How Riemannian Manifolds Converge: A Survey
• The Fundamental Groups of Open Manifolds with Nonnegative Ricci Curvature
• Nonnegative Ricci curvature, splitting at infinity, and first Betti number rigidity
• Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups
• Examples of manifolds of positive Ricci curvature with quadratically nonnegatively curved infinity and infinite topological type
• Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
• The Cut-off Covering Spectrum
• Volume growth and the topology of Gromov-Hausdorff limits