Topology from the differentiable viewpoint /
Mathematician John Milnor provides a 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 homoto...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Princeton, N.J. :
Princeton University Press,
1997
Princeton, N.J. : c1997 Princeton, N.J. : ©1997 Princeton, N.J. : 1997 |
| Edition: | Rev. ed |
| Series: | Princeton landmarks in mathematics and physics
|
| Subjects: |
Table of 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
- App Classifying 1-manifolds
- Bibliography
- Index