Differentiable Structures on the 15-Sphere and Pontrjagin Classes of Certain Manifolds

Abstract

No manifold had been known which can carry two distinct differentiable structures until the recent important contribution due to J. Milnor [7] concerning the 7-sphere appeared. In connection with his work, there are several problems, for example, about the existence of any other manifold with such property, about the topological invariance of the Pontrjagin classes of manifolds, etc.; some of them will be discussed in the present note.