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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)
MathSciNet review: 1483831
MSC: Primary 55P62; Secondary 18E30, 19D55, 19L47, 55N91, 55P42

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Table of Contents


  • 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