Topology from the Differentiable Viewpoint

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Princeton University Press, 1997 - Mathematics - 64 pages
2 Reviews

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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Full of rubbish. Milnor does not know how to impart mathematical knowledge to a fresher having good prerequisites. Perhaps he does not like, others know the subject otherwise his importance woud be diminished.

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Este librito es realmente hermoso, es claro, conciso, y contiene muy buenos ejemplos. Solo se necesitan conocimientos básicos de cálculo y topología para leerlo.
This book is simply beautifull, is
clear, concise, is full of interesting examples. You need as background only basic knowleges of calculus and point set topology. 

Contents

Smooth manifolds and smooth maps
1
The theorem of Sard and Brown
10
Proof of Sards theorem
16
Oriented manifolds
26
Vector fields and the Euler number
32
Framed cobordism the Pontryagin construction
42
Exercises
52
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Page 59 - Debreu, G., Theory of Value, New York, Wiley, 1959. [6] Dhrymes, PJ, On a Class of Utility and Production Functions Yielding Everywhere Differentiable Demand Functions, Review of Economic Studies, 34(1967), 399-408.

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About the author (1997)

John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at SUNY, Stony Brook. He is the author of "Topology from the Differential Viewpoint, Singular Points of Complex Hypersurfaces, Morse Theory, Introduction to Algebraic K-Theory, Characteristic Classes" (with James Stasheff), and "Lectures on the H-Cobordism Theorem" (Princeton).

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