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Topology from the Differentiable Viewpoint
John Milnor

John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters
John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society

Paperback | 1997 | $46.00 | £38.95 | ISBN: 9780691048338
80 pp. | 6 x 9
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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.

Table of Contents:

Preface
1 Smooth manifolds and smooth maps 1
Tangent spaces and derivatives 2
Regular values 7
The fundamental theorem of algebra 8
2 The theorem of Sard and Brown 10
Manifolds with boundary 12
The Brouwer fixed point theorem 13
3 Proof of Sard's theorem 16
4 The degree modulo 2 of a mapping 20
Smooth homotopy and smooth isotopy 20
5 Oriented manifolds 26
The Brouwer degree 27
6 Vector fields and the Euler number 32
7 Framed cobordism; the Pontryagin construction 42
The Hopf theorem 50
8 Exercises 52
App Classifying 1-manifolds 55
Bibliography 59
Index 63

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Hardcover published in 1965

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