DIFFERENTIAL MANIFOLDS KOSINSKI PDF

Antoni A. Kosinski The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifoldspresents 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.

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Product Details 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.

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.

Reprint of the Academic Press, Boston, edition.

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Amazon Inspire Digital Educational Resources. It is possible to do almost everything without them. Lee covers the rudiments quite nicely, and then also gets diffeeential some basic symplectic geometry and Lie groups. Since the purpose of the first 4 chapters about 75 pp is to develop the machinery of differential topology to the point where the results on handles, cobordism, and surgery can be proved, several topics are briefly touched upon that are generally not encountered in introductory diff top books, such as the group Gamma of differential structures on the m-sphere mod those that extend over the m-disk or the bidegree of a map from a product of spheres to a sphere, losinski addition to the aforementioned manidolds of Whitney and Haefliger, but just enough is given so that they may be used in later proofs. Diffeerntial, the proofs are much more brief then those of Lee and Hirsch contains many more typos than Lee.

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KOSINSKI DIFFERENTIAL MANIFOLDS PDF

Product Details 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.

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