Rational S-equivariant Stable Homotopy Theory
American Mathematical Society (Verlag)
978-0-8218-1001-9 (ISBN)
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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 behavior of the Atiyah-Hirzebruch spectral sequence, the structure of $S^1$-equivariant $K$-theory, and the rational behavior of cyclotomic spectra and the topological cyclic homology construction.
General introduction Part I. The algebraic model of rational $/mathbb T$-spectra: Introduction to Part I Topological building blocks Maps between $/mathcal F$-free $/mathbb T$-spectra Categorical reprocessing Assembly and the standard model The torsion model Part II. Change of groups functors in algebra and topology: Introduction to Part II Induction, coinduction and geometric fixed points Algebraic inflation and deflation Inflation, Lewis-May fixed points and quotients Part III. Applications: Introduction to Part III Homotopy Mackey functors and related constructions Classical miscellany Cyclic and Tate cohomology Cyclotomic spectra and topological cyclic cohomology Part IV. Tensor and Hom in algebra and topology: Introduction Torsion functors Torsion functors for the semifree standard model Wide spheres and representing the semifree torsion functor Torsion functors for the full standard model Product functors The tensor-Hom adjunction The derived tensor-Hom adjunction Smash products, function spectra and Lewis-May fixed points Appendix A. Mackey functors Appendix B. Closed model categories Appendix C. Conventions Appendix D. Indices Appendix E. Summary of models Bibliography.
| Erscheint lt. Verlag | 30.3.1999 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-1001-4 / 0821810014 |
| ISBN-13 | 978-0-8218-1001-9 / 9780821810019 |
| Zustand | Neuware |
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