The topology of fibre bundles / by Norman Steenrod.
Series Princeton mathematical series ; 14Editor: Princeton, N.J. : Princeton University Press, 1951Descripción: viii, 229 p. ; cmOtra clasificación: 55-02 (55Rxx)Part I. The General Theory of Bundles -- 1. Introduction [3] -- 2. Coordinate bundles and fibre bundles [2] -- 3. Construction of a bundle from coordinate transformations [14] -- 4. The product bundle [16] -- 5. The Ehresmann-Feldbau definition of bundle [18] -- 6. Differentiable manifolds and tensor bundles [20] -- 7. Factor spaces of groups [28] -- 8. The principal bundle and the principal map [85] -- 9. Associated bundles and relative bundles [43] -- 10. The induced bundle [47] -- 11. Homotopies of maps of bundles [49] -- 12. Construction of cross-sections [51] -- 13. Bundles having a totally disconnected group [59] -- 14. Covering spaces [67] -- Part II. The Homotopy Theory or Bundles -- 15. Homotopy groups [72] -- 16. The operations of on [83] -- 17. The homotopy sequence of a bundle [90] -- 18. The classification of bundles over the n-spherv [96] -- 19. Universal bundles and the classification theorem [100] -- 20. The fibering of spheres by spheres [105] -- 21. The homotopy groups of spheres [110] -- 22. Homotopy groups of the orthogonal groups [114] -- 23. A characteristic map for the bundle over R [118] -- 24. A characteristic map for the bundle over U [124] -- 25. The homotopy groups of miscellaneous manifolds [131] -- 26. Sphere bundles over spheres. [134] -- 27. The tangent bundle of S [140] -- 28. On the non-existence of fiberings of spheres by spheres [144] -- Part III. The Cohomology Theory of Bundles -- 29. The stepwise extension of a cross-section [148] -- 30. Bundles of coefficients [151] -- 31. Cohomology groups based on a bundle of coefficients [155] -- 32. The obstruction cocycle [166] -- 33. The difference cochain [169] -- 34. Extension and deformation theorems [174] -- 35. The primary obstruction and the characteristic cohomology -- class [177] -- 36. The primary difference of two cross-sections [181] -- 37. Extensions of functions, and the homotopy classification of maps I84 -- 38. The Whitney characteristic classes of a sphere bundle [190] -- 39. The Stiefel characteristic classes of differentiable manifolds [199] -- 40. Quadratic forms on manifolds [204] -- 41. Complex analytic manifolds and exterior forms of degree 2 [209] -- Appendix [218] -- Bibliography [223] -- Index [228] --
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| 53 L477-2 Introduction to smooth manifolds / | 53 Sc365 Lectures on differential geometry / | 53 W926 New developments in lie theory and geometry : | 55 St814 The topology of fibre bundles / | 55 W592 Elements of homotopy theory / | 57 M161 The arithmetic of hyperbolic three-manifolds / | 58 Au912 Spinning tops : a course on integrable systems / |
2nd print., 1957. Appendix added.
Part I. The General Theory of Bundles --
1. Introduction [3] --
2. Coordinate bundles and fibre bundles [2] --
3. Construction of a bundle from coordinate transformations [14] --
4. The product bundle [16] --
5. The Ehresmann-Feldbau definition of bundle [18] --
6. Differentiable manifolds and tensor bundles [20] --
7. Factor spaces of groups [28] --
8. The principal bundle and the principal map [85] --
9. Associated bundles and relative bundles [43] --
10. The induced bundle [47] --
11. Homotopies of maps of bundles [49] --
12. Construction of cross-sections [51] --
13. Bundles having a totally disconnected group [59] --
14. Covering spaces [67] --
Part II. The Homotopy Theory or Bundles --
15. Homotopy groups [72] --
16. The operations of on [83] --
17. The homotopy sequence of a bundle [90] --
18. The classification of bundles over the n-spherv [96] --
19. Universal bundles and the classification theorem [100] --
20. The fibering of spheres by spheres [105] --
21. The homotopy groups of spheres [110] --
22. Homotopy groups of the orthogonal groups [114] --
23. A characteristic map for the bundle over R [118] --
24. A characteristic map for the bundle over U [124] --
25. The homotopy groups of miscellaneous manifolds [131] --
26. Sphere bundles over spheres. [134] --
27. The tangent bundle of S [140] --
28. On the non-existence of fiberings of spheres by spheres [144] --
Part III. The Cohomology Theory of Bundles --
29. The stepwise extension of a cross-section [148] --
30. Bundles of coefficients [151] --
31. Cohomology groups based on a bundle of coefficients [155] --
32. The obstruction cocycle [166] --
33. The difference cochain [169] --
34. Extension and deformation theorems [174] --
35. The primary obstruction and the characteristic cohomology --
class [177] --
36. The primary difference of two cross-sections [181] --
37. Extensions of functions, and the homotopy classification of maps I84 --
38. The Whitney characteristic classes of a sphere bundle [190] --
39. The Stiefel characteristic classes of differentiable manifolds [199] --
40. Quadratic forms on manifolds [204] --
41. Complex analytic manifolds and exterior forms of degree 2 [209] --
Appendix [218] --
Bibliography [223] --
Index [228] --
MR, 12,522b
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