In dimension 4, PL and Diff agree, but Top differs. In dimensions above 6 they all differ. In dimensions 5 and 6 every PL manifold admits an infinitely differentiable structure that is so-called Whitehead compatible.
In dimension 4, PL and Diff concur, but Top diverges. In dimensions above 6 they all diverge. In dimensions 5 and 6 every PL manifold admits an infinitely differentiable structure that is known as Whitehead compatible.