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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

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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