Synopses & Reviews
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory.
Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.
"How useful it is," noted the Bulletin of the American Mathematical Society, "to have a single, short, well-written book on differential topology." This volume begins with a detailed, self-contained review of the foundations of differential topology that requires only a minimal knowledge of elementary algebraic topology. Subsequent chapters explain the technique of joining manifolds along submanifolds, the handle presentation theorem, and the proof of the h-cobordism theorem based on these constructions. There follows a chapter on the Pontriagin Construction—the principal link between differential topology and homotopy theory. The final chapter introduces the method of surgery and applies it to the classification of smooth structures of spheres. The text is supplemented by numerous interesting historical notes and contains a new appendix, "The Work of Grigory Perelman," by John W. Morgan, which discusses the most recent developments in differential topology.
Synopsis
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.
Synopsis
"How useful it is," noted the Bulletin of the American Mathematical Society, "to have a single, short, well-written book on differential topology." This accessible volume introduces advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds, from elements of theory to method of surgery. 1993 edition.
Synopsis
Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Table of Contents
IntroductionI. Differentiable StructuresII. Immersions, Imbeddings, SubmanifoldsIII. Normal Bundle, Tubular NeighborhoodsIV. TransversalityV. FoliationsVI. Operations on ManifoldsVII. Handle Presentation TheoremVIII. The h-Cobordism TheoremIX. Framed ManifoldsX. SurgeryAppendix I: Implicit Function Theorem; A Lemma of M. Morse; Brown-Sard Theorem; Orthonormalization; Homotopy Groups of SO(
k)Appendix IIBibliographyIndex