Finiteness theorems for nonnegatively curved vector bundles

2000/02/03 by Igor Belegradek, Vitali Kapovitch, Belegradek, Igor +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0002028

26 pages

arxiv created 2000/02/03 · arxiv updated 2009/11/30

Abstract

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of ``bounded geometry''.

Related

• Vector bundles with infinitely many souls
• Topological finiteness for asymptotically nonnegatively curved manifolds
• Topological obstructions to nonnegative curvature
• Nonnegatively and Positively curved manifolds
• Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics