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Topology from the Differentiable Viewpoint

โœ Scribed by John Willard Milnor


Book ID
127446626
Publisher
University Press Of Virginia
Year
1997
Tongue
English
Weight
1 MB
Category
Library
ASIN
B0012BU0K6

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โœฆ Synopsis


This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.


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The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method