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Topology from the differentiable viewpoint/ John W Milnor

By: Series: Princeton Landmarks in Mathematics and Physics | Princeton Landmarks in MathematicsPublication details: Princeton: Princeton University Press, 1997Edition: revDescription: ix, 64 pages; 23 cmISBN:
  • 9780691048339
Subject(s): DDC classification:
  • 23rd 514.72 M659
Contents:
Preface -- Smooth manifolds and smooth maps -- The theorem of Sard and Brown -- Proof of Sard's theorem -- The degree modulo 2 of a mapping -- Oriented manifolds -- Vector fields and the Euler number -- Framed cobordism: the Pontryagin construction -- Exercises
Summary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 514.72 M659 (Browse shelf(Opens below)) Available 138669
Total holds: 0

The content of the book is based on notes by David W Weaver

Includes bibliography and index

Preface -- Smooth manifolds and smooth maps -- The theorem of Sard and Brown -- Proof of Sard's theorem -- The degree modulo 2 of a mapping -- Oriented manifolds -- Vector fields and the Euler number -- Framed cobordism: the Pontryagin construction -- Exercises

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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