Topology from the differentiable viewpoint

By: Milnor, John WMaterial type: TextTextSeries: Princeton landmarks in mathematics and physicsPublication details: Princeton, N.J. : Princeton University Press, ©1997Description: ix, 64 pages : illustrationsISBN: 9780691048338; 0691048339 Subject(s): Differential topologyDDC classification: 514.72
Contents:
Preface -- 1. Smooth manifolds and smooth maps -- Tangent spaces and derivatives -- Regular values -- The fundamental theorem of algebra -- 2. The theorem of Sard and Brown -- Manifolds with boundary -- The Brouwer fixed point theorem -- 3. Proof of Sard's theorem -- 4. The degree modulo 2 of a mapping -- Smooth homotopy and smooth isotopy -- 5. Oriented manifolds -- The Brouwer degree -- 6. Vector fields and the Euler number -- 7. Framed cobordism the Pontryagin construction -- The Hopf theorem -- 8. Exercises --
Summary: Provides a clear introduction to one of the important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, this book goes on to examine tangent spaces, oriented manifolds, and vector fields. It discusses concepts such as homotopy, the index number of a map, and the Pontryagin construction
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Item type Current library Collection Call number Status Date due Barcode Item holds
Reference Books Reference Books Main Library
Reference 		Reference 514.72 MIL (Browse shelf(Opens below)) Available 009748
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Includes Index

Preface --
1. Smooth manifolds and smooth maps --
Tangent spaces and derivatives --
Regular values --
The fundamental theorem of algebra --
2. The theorem of Sard and Brown --
Manifolds with boundary --
The Brouwer fixed point theorem --
3. Proof of Sard's theorem --
4. The degree modulo 2 of a mapping --
Smooth homotopy and smooth isotopy --
5. Oriented manifolds --
The Brouwer degree --
6. Vector fields and the Euler number --
7. Framed cobordism the Pontryagin construction --
The Hopf theorem --
8. Exercises --


Provides a clear introduction to one of the important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, this book goes on to examine tangent spaces, oriented manifolds, and vector fields. It discusses concepts such as homotopy, the index number of a map, and the Pontryagin construction

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