Download or read book Topology from the Differentiable Viewpoint written by John Willard Milnor and published by Princeton University Press. This book was released on 1997-12-14 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.