About:

One of the milestones in the study of high-dimensional manifolds is Milnor's discovery of exotic spheres (that is, smooth manifolds that are homeomorphic but not diffeomorphic to the standard sphere) [Mil56], and their classification in homotopy theoretical terms due to Kervaire and Milnor [KM63]. The goal of these lectures is to explain Milnor's construction of an exotic 7-sphere and Kervaire-Milnor's approach to the classification of these spheres in every dimension. Along the way, we will touch on several central techniques in manifold topology such as characteristic classes, bordism theory, and surgery.