从微积分到上同调PDF电子书下载

Chapter 1 Introduction 1

Chapter 2 The Alternating Algebra 7

Chapter 3 de Rham Cohomology 15

Chapter 4 Chain Complexes and their Cohomology 25

Chapter 5 The Mayer-Vietoris Sequence 33

Chapter 6 Homotopy 39

Chapter 7 Applications of de Rham Cohomology 47

Chapter 8 Smooth Manifolds 57

Chapter 9 Differential Forms on Smoth Manifolds 65

Chapter 10 Integration on Manifolds 83

Chapter 11 Degree,Linking Numbers and Index of Vector Fields 97

Chapter 12 The Poincaré-Hopf Theorem 113

Chapter 13 PoincaréDuality 127

Chapter 14 The Complex Projective Space CPn 139

Chapter 15 Fiber Bundles and Vector Bundles 147

Chapter 16 Operations on Vector Bundles and their Sections 157

Chapter 17 Connections and Curvature 167

Chapter 18 Characteristic Classes of Complex Vector Bundles 181

Chapter 19 The Euler Class 193

Chapter 20 Cohomology of Projective and Grassmannian Bundles 199

Chapter 21 Thom Isomorphism and the General Gauss-Bonnet Formula 211

Appendix A Smooth Partition of Unity 221

Appendix B Invariant Polynomials 227

Appendix C Proof of Lemmas 12.12 and 12.13 233

Appendix D Exercises 243

References 281

Index 283