Memoirs of the American Mathematical Society 1999; 289 pp; softcover Volume: 138 ISBN10: 0821810014 ISBN13: 9780821810019 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/138/661
 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 AtiyahHirzebruch 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 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, LewisMay 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 tensorHom adjunction
 The derived tensorHom adjunction
 Smash products, function spectra and LewisMay fixed points
 Appendix A. Mackey functors
 Appendix B. Closed model categories
 Appendix C. Conventions
 Appendix D. Indices
 Appendix E. Summary of models
 Bibliography
