Topology from the Differentiable Viewpoint

By: John Milnor

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Paperback | 23 February 1998

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80 Pages

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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.

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Non-Fiction Mathematics Geometry Topology Algebraic Topology Analytic Topology

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

Topology from the Differentiable Viewpoint

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