Topology from the Differentiable Viewpoint

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Princeton University Press, 1997/12/14 - 64 ページ

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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Topology from the Differentiable Viewpoint (Princeton Landmarks in Mathematics)のQ.E.D.さんの感想・レビュー

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美しい本です。サードの定理の証明はこの本を参照するのが良いと思います。薄い本の割には内容が濃く、緻密に読み進めました。演習問題が17題載っています。 レビュー全文を読む

目次

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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人気のある引用

59 ページ - 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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