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Preface

1 Introduction
1£®1 A Robot's Arm
1£®2 The Configuration Space of Two Electrons
1£®3 State Spaces and Fiber Bundles
1£®4 Further Examples
1£®5 Compact Surfaces
1£®6 Higher Dimensions

2 Smooth Manifolds
2£®1 Topological Manifolds
2£®2 Smooth Structures
2£®3 Maximal Atlases
2£®4 Smooth Maps
2£®5 Submanifolds
2£®6 Products and Sums

3 The Tangent Space
3£®1 Germs
3£®2 Smooth Bump Functions
3£®3 The Tangent Space
3£®4 The Cotangent Space
3£®5 Derivations

4 Regular Values
4£®1 The Rank
4£®2 The Inverse Function Theorem
4£®3 The Rank Theorem
4£®4 Regular Values
4£®5 Transversality
4£®6 Sard's Theorem
4£®7 Immersions and Imbeddings

5 Vector Bundles
5£®1 Topological Vector Bundles
5£®2 Transition Functions
5£®3 Smooth Vector Bundles
5£®4 Pre-vector Bundles
5£®5 The Tangent Bundle
5£®6 The Cotangent Bundle
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6 Constructions on Vector Bundles
7 Integrability
8 Local Phenomena that Go Global

Appendix A Point Set Topology
References
Index