§6. A Cell Structure for Grassmann Manifolds

Chapters in this book

1. Frontmatter i
2. Preface v
3. Contents vii
4. §1. Smooth Manifolds 1
5. §2. Vector Bundles 13
6. §3. Constructing New Vector Bundles Out of Old 25
7. §4. Stiefel-Whitney Classes 37
8. §5. Grassmann Manifolds and Universal Bundles 55
9. §6. A Cell Structure for Grassmann Manifolds 73
10. §7. The Cohomology Ring H*(G_n; Z/2) 83
11. §8. Existence of Stiefel-Whitney Classes 89
12. §9. Oriented Bundles and the Euler Class 95
13. §10. The Thom Isomorphism Theorem 105
14. §11. Computations in a Smooth Manifold 115
15. §12. Obstructions 139
16. §13. Complex Vector Bundles and Complex Manifolds 149
17. §14. Chern Classes 155
18. §15. Pontrjagin Classes 173
19. §16. Chern Numbers and Pontrjagin Numbers 183
20. §17. The Oriented Cobordism Ring Ω_* 199
21. §18. Thom Spaces and Transversality 205
22. §19. Multiplicative Sequences and the Signature Theorem 219
23. §20. Combinatorial Pontrjagin Classes 231
24. Epilogue 249
25. Appendix A: Singular Homology and Cohomology 257
26. Appendix B: Bernoulli Numbers 281
27. Appendix C: Connections, Curvature, and Characteristic Classes 289
28. Bibliography 315
29. Index 325