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The $mod 2$ cohomology structure of certain fibre spaces
About this Title
W. S. Massey and F. P. Peterson
Publication: Memoirs of the American Mathematical Society
Publication Year:
1967; Number 74
ISBNs: 978-0-8218-1274-7 (print); 978-1-4704-0022-4 (online)
DOI: https://doi.org/10.1090/memo/0074
MathSciNet review: 0226637
Table of Contents
Chapters
- 1. Introduction
- Part I. Some basic results
- 2. Summary of results of the previous paper
- 3. The structure of $\textrm {Tor}_n^R(M,N)$ as a module over the Steenrod algebra
- 4. Statement of the main theorem
- 5. The structure of the module $M(\xi )$
- 6. Proof of Proposition 4.2
- 7. Naturality properties
- 8. Product of two fibre bundles
- 9. Behavior under the suspension homomorphism
- Part II. Two-stage Postnikov systems
- 10. $\lambda$-modules
- 11. Application of the theory of $\lambda$-modules to fibre spaces
- 12. Application to 2-stage Postnikov systems with stable $k$-invariants
- 13. The functor $\Omega$
- 14. The structure of the algebra $R$ and the module $M(\xi )$ in the case of a stable 2-stage Postnikov system
- 15. Simplification of the extension problem under hypotheses (i)–(vii)
- 16. Re-interpretation of the results of Sec. 15 in the case of 2-stage Postnikov systems with stable mod 2 $k$-invariant
- 17. Naturality of the fundamental sequence
- 18. The product of two Postnikov systems
- 19. Effect of the suspension homomorphism
- 20. Utilization of the $H$-space structure
- 21. Examples
- 22. The Noetherian property of unstable $A$-modules
- Part III. The unstable Adams spectral sequence
- 23. The main results of Part III
- 24. Unstable projective resolutions
- 25. Adams-Postnikov systems
- 26. The spectral sequence
- 27. Convergence statements
- 28. Appendix