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Topology from the Differentiable Viewpoint (Princeton Landmarks in Mathematics & Physics)

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Synopses & Reviews

Publisher Comments:

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.

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.

Table of Contents

Preface
1Smooth manifolds and smooth maps1
Tangent spaces and derivatives2
Regular values7
The fundamental theorem of algebra8
2The theorem of Sard and Brown10
Manifolds with boundary12
The Brouwer fixed point theorem13
3Proof of Sard's theorem16
4The degree modulo 2 of a mapping20
Smooth homotopy and smooth isotopy20
5Oriented manifolds26
The Brouwer degree27
6Vector fields and the Euler number32
7Framed cobordism; the Pontryagin construction42
The Hopf theorem50
8Exercises52
AppClassifying 1-manifolds55
Bibliography59
Index63

Product Details

ISBN:
9780691048338
Author:
Milnor, John
Publisher:
Princeton University Press
Author:
Milnor, John Willard
Location:
Princeton, N.J. :
Subject:
Advanced
Subject:
Topology
Subject:
Differential topology
Subject:
Topology - General
Subject:
Physics
Subject:
Mathematics
Subject:
MATHEMATICS / Topology
Copyright:
Edition Description:
Trade paper
Series:
Princeton Landmarks in Mathematics & Physics
Series Volume:
105-90
Publication Date:
November 1997
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
80
Dimensions:
9 x 6 in 5 oz

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Related Subjects


Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Topology from the Differentiable Viewpoint (Princeton Landmarks in Mathematics & Physics) New Trade Paper
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Product details 80 pages Princeton University Press - English 9780691048338 Reviews:
"Synopsis" by , 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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