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Topology of Surfaces, Knots, and Manifolds
Posted on 2010-03-16
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More : Stephan C. Carlson offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links--the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a book that provides solid coverage of the mathematics underlying these topics.Review: This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and there are superfluous examples. The exercises in the text are well thought out and are not extremely difficult. The exercises complement the text very well. The text makes clear a lot of difficult concepts such as isotopic surfaces as opposed to homeomorphic surfaces. I particularly enjoyed the manner in which the topology of knots was explained. After reading this text, the reader should be able to better visualize the projective plain and even the Klein bottle as it exists in 4-dimensional space. I have not read a text on topology that I enjoyed reading as much since Munkres. This text is a must have for any topologist Quote: I Have Put A Lot Of Time And Hard Work On This Upload & Post
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