| 《纤维丛拓扑学(英文版)》 part i. the general theory of bundles 1. introduction 2. coordinate bundles and fibre bundles 3. construction of a bundle from coordinate transformations 4. the product bundle 5. the ehresmann-feldbau definition of bundle. 6. differentiable manifolds and tensor bundles 7. factor spaces of groups 8. the principal bundle and the principal map 9. associated bundles and relative bundles 10. the induced bundle 11. homotopies of maps of bundles. 12. construction of cross-sections 13. bundles having a totally disconnected group. 14. covering spaces part ii. the homotopy theory of bundles 15. homotopy groups 16. the operations of π1 on πn 17. the homotopy sequence of a bundle .18. the classification of bundles over the n-sphere 19. universal bundles and the classification theorem. 20. the fibering of spheres by spheres 21. the homotopy groups of spheres 22. homotopy groups of the orthogonal groups 23. a characteristic map for the bundle rn+1 over sn 24. a characteristic map for the bundle un over s2n-1 25. the homotopy groups of miscellaneous manifolds 26. sphere bundles over spheres. 27. the tangent bundle of sn 28. on the non-existence of fiberings of spheres by spheres part iii. the cohomology theory of bundles 29. the stepwise extension of a cross-section 30. bundles of coefficients 31. cohomology groups based on a bundle of coefficients 32. the obstruction cocycle 33. the difference cochain 34. extension and deformation theorems 35. the primary obstruction and the characteristic cohomology class. 36. the primary difference of two cross-sections 37. extensions of functions, and the homotopy classification of maps. 38. the whitney characteristic classes of a sphere bundle 39. the stiefel characteristic classes of differentiable manifolds 40. quadratic forms on manifolds 41. complex analytic manifolds and exterior forms of degree 2. appendix bibliography index |
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