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."
"Finiteness theorems for nonnegatively curved vector bundles." Duke Math. J. 108 (1) 109 - 134, 15 May 2001. https://doi.org/10.1215/S0012-7094-01-10813-2