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The $\mod 2$ Cohomology Structure of Certain Fibre Spaces
| eBook ISBN: | 978-1-4704-0022-4 |
| Product Code: | MEMO/1/74.E |
| List Price: | $20.00 |
| MAA Member Price: | $18.00 |
| AMS Member Price: | $12.00 |
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The $\mod 2$ Cohomology Structure of Certain Fibre Spaces
| eBook ISBN: | 978-1-4704-0022-4 |
| Product Code: | MEMO/1/74.E |
| List Price: | $20.00 |
| MAA Member Price: | $18.00 |
| AMS Member Price: | $12.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1967; 97 ppMSC: Primary 55
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Table of Contents
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Chapters
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1. Introduction
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Part I. Some basic results
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2. Summary of results of the previous paper
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3. The structure of $\textrm {Tor}_n^R(M,N)$ as a module over the Steenrod algebra
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4. Statement of the main theorem
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5. The structure of the module $M(\xi )$
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6. Proof of Proposition 4.2
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7. Naturality properties
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8. Product of two fibre bundles
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9. Behavior under the suspension homomorphism
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Part II. Two-stage Postnikov systems
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10. $\lambda $-modules
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11. Application of the theory of $\lambda $-modules to fibre spaces
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12. Application to 2-stage Postnikov systems with stable $k$-invariants
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13. The functor $\Omega $
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14. The structure of the algebra $R$ and the module $M(\xi )$ in the case of a stable 2-stage Postnikov system
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15. Simplification of the extension problem under hypotheses (i)–(vii)
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16. Re-interpretation of the results of Sec. 15 in the case of 2-stage Postnikov systems with stable mod 2 $k$-invariant
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17. Naturality of the fundamental sequence
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18. The product of two Postnikov systems
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19. Effect of the suspension homomorphism
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20. Utilization of the $H$-space structure
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21. Examples
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22. The Noetherian property of unstable $A$-modules
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Part III. The unstable Adams spectral sequence
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23. The main results of Part III
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24. Unstable projective resolutions
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25. Adams-Postnikov systems
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26. The spectral sequence
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27. Convergence statements
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28. Appendix
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
-
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
Review Copy – for publishers of book reviews
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