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.

survey 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 (4)

• The Fundamental Groups of Open Manifolds with Nonnegative Ricci Curvature
• Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
• Volume growth and the topology of Gromov-Hausdorff limits
• Nonnegative Ricci curvature, splitting at infinity, and first Betti number rigidity