Differential Manifolds

9780124218505

0124218504

Differential Manifolds 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 the theory of lie groups. 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 individual study. Key Features * Presents the study and classification of smooth structures on manifolds * It begins with the elements of theory and concludes with an introduction to the method of surgery * Chapters 1-5 contain a detailed presentation of the foundations of differential topology--no knowledge of algebraic 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-cobordism theory * Chapter 9 presents the Pontriagrin construction, the principle link between differential topology and homotopy theory; The final chapter introduces the method of surgery and applies it to the classification of smooth structures on spheres