Author(s)

Bibliographic Information

Topology from the differentiable viewpoint

John W. Milnor ; based on notes by David W. Weaver

(Princeton landmarks in mathematics and physics)(Princeton paperbacks)

Princeton University Press, 1997

Rev. ed

  • : pbk

Available at  / 55 libraries

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Note

Originally published: Charlottesville : University Press of Virginia, 1965

Includes bibliographical references (p. [59]-61) and index

Description and Table of Contents

Description

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

  • Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed point theorem133Proof of Sard's theorem164The degree modulo 2 of a mapping20Smooth homotopy and smooth isotopy205Oriented manifolds26The Brouwer degree276Vector fields and the Euler number327Framed cobordism
  • the Pontryagin construction42The Hopf theorem508Exercises52AppClassifying 1-manifolds55Bibliography59Index63

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