The Topology of Stiefel Manifolds
The Topology of Stiefel Manifolds
I. M. James
January 1977
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Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard University, describe the state of knowledge of the subject, as well as the outstanding problems. The emphasis throughout is on applications (within the subject) rather than on theory. However, such theory as is required is summarized and references to the literature are given, thus making the book accessible to non-specialists and particularly graduate students. Many examples are given and further problems suggested.
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Table of Contents
- 1. Introduction: algebra versus topology
- 2. The Stiefel manifolds
- 3. The auxiliary spaces
- 4. Retractible fibrations
- 5. Thom spaces
- 6. Homotopy equivariance
- 7. Cross-sections and the S-type
- 8. Relative Stiefel manifolds
- 9. Cannibalistic characteristic classes
- 10. Exponential characteristic classes
- 11. The main theorem of J-theory
- 12. The fibre suspension
- 13. Canonical automorphisms
- 14. The iterated suspension
- 15.Samelson products
- 16. The Hopf construction
- 17. The Bott suspension
- 18. The intrinsic join again
- 19. Homotopy- commutativity
- 20. The triviality problem
- 21. When is Pn, k neutral?
- 22. When is V n, 2 neutral?
- 23. When is V n, k neutral?
- 24. Further results and problems
