The Topology of Stiefel Manifolds (London Mathematical Society Lecture Note Series, Series Number 24)

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. Cover; Title; Copyright; Contents; Preface; 1. Introduction: algebra versus topology; 2. The Stiefel manifolds; 3. The auxiliary spaces; 4. Retractible fibrations; 5. Thorn 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 Professor Ioan James gives a very good review of developments in the area, a lot of which he personally helped to invent or developed. He continues with his tradition in writing clear and concise books (like Topological and Uniform Spaces, by Springer-Verlag) and gives the readers a clear look into various aspects of Stiefel manifolds. It is a good chance to hear from one of the few leading experts in this specialist field of mathematics. 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 present state of knowledge of the subject, as well as the outstanding problems.