AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Rational $S^{1}$-equivariant stable homotopy theory
About this Title
J. P. C. Greenlees
Publication: Memoirs of the American Mathematical Society
Publication Year:
1999; Volume 138, Number 661
ISBNs: 978-0-8218-1001-9 (print); 978-1-4704-0250-1 (online)
DOI: https://doi.org/10.1090/memo/0661
MathSciNet review: 1483831
MSC: Primary 55P62; Secondary 18E30, 19D55, 19L47, 55N91, 55P42
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