Hi everyone, im reading Milnor's article "On manifolds homeomorphic to the 7-sphere", in which he constructs the first example of an exotic structure, id like to know if there's a particular reason why Pontrjagin classes become so relevant in defining the invariant that "detects" exotic smoothness. More generally, is there a way to interpret the Pontrjagin classes that connects them with the way the smooth structure of the manifold behaves? Or are they just happy coincidences and the most "geometric" meaning you can get from them is the obstruction of finding n-k-2 linearly independent sections on the tangent bundle? References are much appreciated! Thanx in advance