Milnor's sphere

Milnor's sphere refers to a specific example of a manifold that was discovered by mathematician John Milnor in the 1950s. It is particularly known for being a counterexample in differential topology, specifically in the context of the classification of high-dimensional spheres. In more detail, Milnor constructed a manifold that is homeomorphic (topologically equivalent) to the 7-dimensional sphere \( S^7 \) but not diffeomorphic (smoothly equivalent) to it.