Finiteness theorems for nonnegatively curved vector bundles

TL;DR

This paper establishes finiteness theorems for the normal bundles of souls in nonnegatively curved manifolds, extending to open manifolds with topology concentrated on bounded geometry domains.

Contribution

It introduces new finiteness results for normal bundles in nonnegatively curved manifolds and for open manifolds with bounded geometry topology.

Findings

Finiteness theorems for normal bundles to souls in nonnegatively curved manifolds

Finiteness results for open manifolds with topology on bounded geometry domains

Extension of finiteness results to broader classes of manifolds

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''.