Topology from the Differentiable Viewpoint

Topology from the Differentiable Viewpoint......Page 3
Copyright......Page 4
Preface......Page 7
Contents......Page 9
1. Smooth manifolds and smooth maps......Page 13
Tangent spaces and derivatives......Page 14
Regular values......Page 19
The fundamental theorem of algebra......Page 20
2. The theorem of Sard and Brown......Page 22
Manifolds with boundary......Page 24
The Brouwer fixed point theorem......Page 25
3. Proof of Sard's theorem......Page 28
Smooth homotopy and smooth isotopy......Page 32
5. Oriented manifolds......Page 38
The Brouwer degree......Page 39
6. Vector fields and the Euler number......Page 44
7. Framed cobordism; the Pontryagin construction......Page 54
The Hopf theorem......Page 62
8. Exercises......Page 64
Appendix: Classifying 1-Manifolds......Page 67
Bibliography......Page 71
Index......Page 75