Page "Differential topology" Paragraph 2

On the other hand, smooth manifolds are more rigid than the topological manifolds.

John Milnor discovered that some spheres have more than one smooth structure — see exotic sphere and Donaldson's theorem.

Kervaire exhibited topological manifolds with no smooth structure at all.

Some constructions of smooth manifold theory, such as the existence of tangent bundles, can be done in the topological setting with much more work, and others cannot.