| eBook ISBN: | 978-1-4704-0250-1 |
| Product Code: | MEMO/138/661.E |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $43.80 |
| eBook ISBN: | 978-1-4704-0250-1 |
| Product Code: | MEMO/138/661.E |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $43.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 138; 1999; 289 ppMSC: Primary 55; Secondary 18; 19; 20
The memoir presents a systematic study of rational \(S^1\)-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of \(S^1\)-equivariant \(K\)-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.
ReadershipGraduate students and research mathematicians working in algebraic topology.
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Table of Contents
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Chapters
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0. General introduction
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I. The algebraic model of $\mathbb {T}$-spectra
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1. Introduction to Part I
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2. Topological building blocks
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3. Maps between $\mathcal {F}$-free $\mathbb {T}$-spectra
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4. Categorical reprocessing
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5. Assembly and the standard model
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6. The torsion model
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II. Change of groups functors in algebra and topology
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7. Introduction to Part II
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8. Induction, coinduction and geometric fixed points
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9. Algebraic inflation and deflation
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10. Inflation, Lewis-May fixed points and quotients
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III. Applications
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11. Introduction to Part III
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12. Homotopy Mackey functors and related constructions
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13. Classical miscellany
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14. Cyclic and Tate cohomology
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15. Cyclotomic spectra and topological cyclic cohomology
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IV. Tensor and Hom in algebra and topology
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16. Introduction
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17. Torsion functors
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18. Torsion functors for the semifree standard model
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19. Wide spheres and representing the semifree torsion functor
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20. Torsion functors for the full standard model
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21. Product functors
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22. The tensor-Horn adjunction
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23. The derived tensor-Horn adjunction
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24. Smash products, function spectra and Lewis-May fixed points
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The memoir presents a systematic study of rational \(S^1\)-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of \(S^1\)-equivariant \(K\)-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.
Graduate students and research mathematicians working in algebraic topology.
-
Chapters
-
0. General introduction
-
I. The algebraic model of $\mathbb {T}$-spectra
-
1. Introduction to Part I
-
2. Topological building blocks
-
3. Maps between $\mathcal {F}$-free $\mathbb {T}$-spectra
-
4. Categorical reprocessing
-
5. Assembly and the standard model
-
6. The torsion model
-
II. Change of groups functors in algebra and topology
-
7. Introduction to Part II
-
8. Induction, coinduction and geometric fixed points
-
9. Algebraic inflation and deflation
-
10. Inflation, Lewis-May fixed points and quotients
-
III. Applications
-
11. Introduction to Part III
-
12. Homotopy Mackey functors and related constructions
-
13. Classical miscellany
-
14. Cyclic and Tate cohomology
-
15. Cyclotomic spectra and topological cyclic cohomology
-
IV. Tensor and Hom in algebra and topology
-
16. Introduction
-
17. Torsion functors
-
18. Torsion functors for the semifree standard model
-
19. Wide spheres and representing the semifree torsion functor
-
20. Torsion functors for the full standard model
-
21. Product functors
-
22. The tensor-Horn adjunction
-
23. The derived tensor-Horn adjunction
-
24. Smash products, function spectra and Lewis-May fixed points
