The Topology of Stiefel Manifolds

Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists.

I. M. James (Author)

9780521213349, Cambridge University Press

Paperback, published 6 January 1977

180 pages
22.9 x 15.2 x 1.1 cm, 0.265 kg

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.

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

Subject Areas: Geometry [PBM]