On the Construction of Exotic Spheres

Abstract

J. Milnor has proved that the 7-sphere possesses several distinct differentiable structures, and constructed them. This is the first example which is homeomorphic but not diffeomorphic to the standard sphere. Now, it is a well-known fact that there are 28 differentiable structures on the 7-sphere, and Brieskorn constructed all these 7-spheres in another way. In this thesis, we study the way of construction of these spheres. Furthermore, we want to construct all 7-dimensional and 11-dimensional spheres up to diffeomorphism.