John Milnor

Topology from the Differentiable Viewpoint

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Princeton Landmarks in Mathematics and Physics
• Verlag: Princeton University Press
• Seitenzahl: 78
• Erscheinungstermin: 14. Dezember 1997
• Englisch
• Abmessung: 229mm x 152mm x 5mm
• Gewicht: 138g
• ISBN-13: 9780691048338
• ISBN-10: 0691048339
• Artikelnr.: 21455321

Autorenporträt

John Milnor

Inhaltsangabe

Preface
1
Smooth manifolds and smooth maps
1
Tangent spaces and derivatives
2
Regular values
7
The fundamental theorem of algebra
8
2
The theorem of Sard and Brown
10
Manifolds with boundary
12
The Brouwer fixed point theorem
13
3
Proof of Sard's theorem
16
4
The degree modulo 2 of a mapping
20
Smooth homotopy and smooth isotopy
20
5
Oriented manifolds
26
The Brouwer degree
27
6
Vector fields and the Euler number
32
7
Framed cobordism; the Pontryagin construction
42
The Hopf theorem
50
8
Exercises
52
App
Classifying 1-manifolds
55
Bibliography
59
Index
63