内容

目次

Part I. THE GENERAL THEORY OF BUNDLES 1. Introduction 3 2. Coordinatebundles and fibre bundles 6 3. Construction of a bundle from coordinatetransformations 14 4. The product bundle 16 5. The Ehresmann-Feldbaudefinition of bundle 18 6. Differentiable manifolds and tensor bundles 207. Factor spaces of groups 28 8. The principal bundle and the principal map35 9. Associated bundles and relative bundles 43 10. The induced bundle 4711. Homotopies of maps of bundles 49 12. Construction of cross-sections 5413. Bundles having a totally disconnected group 59 14. Covering spaces 67Part II. THE HOMOTOPY THEORY OF BUNDLES 15. Homotopy groups 72 16. Theoperations of Pi1 on Pi n 83 17. The homotopy sequence of a bundle 90 18.The classification of bundles over the n-sphere 96 19. Universal bundles andthe classification theorem 100 20. The fibering of spheres by spheres 10521. The homotopy groups of spheres 110 22. Homotopy groups of the orthogonalgroups 114 23. A characteristic map for the bundle Rn+1 over S n 118 24. Acharacteristic map for the bundle Un over S 2n - 1 124 25. The homotopygroups of miscellaneous manifolds 131 26. Sphere bundles over spheres 13427. The tangent bundle of S n 140 28. On the non-existence of fiberings ofspheres by spheres 144 Part III. THE COHOMOLOGY THEORY OF BUNDLES 29. Thestepwise extension of a cross-section 148 30. Bundles of coefficients 15131. Cohomology groups based on a bundle of coefficients 155 32. Theobstruction cocycle 166 33. The difference cochain 169 34. Extension anddeformation theorems 174 35. The primary obstruction and the characteristiccohomology class 177 36. The primary difference of two cross-sections 18137. Extensions of functions, and the homotopy classification of maps 184 38.The Whitney characteristic classes of a sphere bundle 190 39. The Stiefelcharacteristic classes of differentiable manifolds 199 40. Quadratic formson manifolds 204 41. Complex analytic manifolds and exterior forms of degree2 209 Appendix 218 Bibliography 223 Index 228