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Rational $S^1$-Equivariant Stable Homotopy Theory
 
J. P. C. Greenlees University of Sheffield, England
Rational S^1-Equivariant Stable Homotopy Theory
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
Rational S^1-Equivariant Stable Homotopy Theory
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Rational $S^1$-Equivariant Stable Homotopy Theory
J. P. C. Greenlees University of Sheffield, England
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1381999; 289 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians working in algebraic topology.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1381999; 289 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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