Topology from the Differentiable Viewpoint

by John Milnor

Overview

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.

Product Details

ISBN-13:	9780691048338
Publisher:	Princeton University Press
Publication date:	12/14/1997
Series:	Princeton Landmarks in Mathematics and Physics , #21
Edition description:	REVISED
Pages:	80
Product dimensions:	5.80(w) x 8.80(h) x 0.30(d)

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

Editorial Reviews

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

From the Publisher