Topology from the Differentiable Viewpoint

ISBN-10: 0691048339
ISBN-13: 9780691048338
Edition: 1998
Authors: John Milnor
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Description: 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  More...

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Book details

Copyright year: 1998
Publisher: Princeton University Press
Publication date: 12/14/1997
Binding: Paperback
Pages: 80
Size: 6.25" wide x 9.25" long x 0.25" tall
Weight: 0.506

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.

Preface
Smooth manifolds and smooth maps
Tangent spaces and derivatives
Regular values
The fundamental theorem of algebra
The theorem of Sard and Brown
Manifolds with boundary
The Brouwer fixed point theorem
Proof of Sard's theorem
The degree modulo 2 of a mapping
Smooth homotopy and smooth isotopy
Oriented manifolds
The Brouwer degree
Vector fields and the Euler number
Framed cobordism the Pontryagin construction
The Hopf theorem
Exercises
App Classifying 1-manifolds
Bibliography
Index

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