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 …… 6 Constructions on Vector Bundles 7 Integrability 8 Local Phenomena that Go Global Appendix A Point Set Topology References Index
鄂公網(wǎng)安備 42010302001612號 