Differential Manifold. Pure and Applied Mathematics: A Series of Monographs and Textbooks, Volume 138.
"e;Differential Manifolds"e; is a modern graduate-level introduction to the important field of differential topology. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and complex analysis. The book introduces both the h-cobordism theorem and the classification of differential structures on spheres. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individuals. It presents the study and classification of smooth structures on manifolds and begins with the elements of theory and concludes with an introduction to the method of surgery. Chapters 1-5 contain a details presentation of the foundations of differential topology - no knowledge of algebric topology is required for this self-contained section. Chapters 6-8 begin by explaining the joining of manifolds along submanifolds and ends with the proof of the h-cobordiam theory. The final chapter presents the pontagrin construction the principle link between differential topology and homotopy theory.
