13 citations · 59 across the 34 of their papers we have counts for
5 papers · 2 filters
Obstructions to nonnegative curvature and rational homotopy theory
Igor Belegradek, Vitali Kapovitch
We establish a link between rational homotopy theory and the problem which vector bundles admit complete Riemannian metric of nonnegative sectional curvature. As an application, we…
On Mostow rigidity for variable negative curvature
Igor Belegradek
We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension …
Finiteness theorems for nonnegatively curved vector bundles
Igor Belegradek, Vitali Kapovitch
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 w…
Pinching, Pontrjagin classes, and negatively curved vector bundles
Igor Belegradek
We prove several finiteness results for the class of -manifolds that have fundamental groups isomorphic to and that can be given complete Riemannian metrics of…
Topological obstructions to nonnegative curvature
Igor Belegradek, Vitali Kapovitch
We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construc…