  We discuss topological rigidity of vector bundles with asymptotically conical
(AC) total spaces of rank greater than 1 with a sufficiently connected link;
our focus will mainly be on ALE (asymptotically locally Euclidean) bundles.
Within the smooth category, we topologically classify all ALE tangent bundles
by showing only 2-sphere, projective plane and open contractible manifolds
admit ALE tangent bundles. We also discuss other interesting topological and
geometric rigidities of ALE vector bundles.
