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OverviewThe 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. Full Product DetailsAuthor: Antoni a KosinskiPublisher: Dover Publications Inc. Imprint: Dover Publications Inc. Dimensions: Width: 13.50cm , Height: 1.40cm , Length: 21.40cm Weight: 0.301kg ISBN: 9780486462448ISBN 10: 0486462447 Pages: 288 Publication Date: 28 December 2007 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction I. Differentiable Structures II. Immersions, Imbeddings, Submanifolds III. Normal Bundle, Tubular Neighborhoods IV. Transversality V. Foliations VI. Operations on Manifolds VII. Handle Presentation Theorem VIII. The h-Cobordism Theorem IX. Framed Manifolds X. Surgery Appendix I: Implicit Function Theorem; A Lemma of M. Morse; Brown-Sard Theorem; Orthonormalization; Homotopy Groups of SO(k) Appendix II Bibliography IndexReviewsAuthor InformationAntoni A. Kosinski is Professor Emeritus of Mathematics at Rutgers University. Tab Content 6Author Website:Countries AvailableAll regions |
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