Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees

• Record Nr.: UNINA9910481049303321
• Autore: Greenlees J. P. C (John Patrick Campbell), <1959->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1999
• ISBN: 1-4704-0250-5
• Descrizione fisica: 1 online resource (306 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 661
• Disciplina: 510 s; 514/.24
• Soggetti: Homotopy theory; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "March 1999, volume 138, number 661 (end of volume)."
• Nota di bibliografia: Includes bibliographical references (pages 289) and indexes.
• Nota di contenuto: ""Contents""; ""Chapter 0. General Introduction""; ""0.1. Motivation""; ""0.2. Overview""; ""Part I. The algebraic model of rational T-spectra""; ""Chapter 1. Introduction to Part I""; ""1.1. Outline of the algebraic models""; ""1.2. Reading Guide for Part I""; ""1.3. Haeberly's example""; ""1.4. McClure's Chern character isomorphism for F-spaces""; ""Chapter 2. Topological building blocks""; ""2.1. Natural cells and basic cells""; ""2.2. Separating isotropy types""; ""2.3. The single strand spectra E(H)""; ""2.4. Operations: self-maps of E(H)""; ""Chapter 3. Maps between F-free T-spectra""; ""3.1. The Adams short exact sequence""""3.2. The Whitehead and Hurewicz theorems for T-spectra over H""; ""3.3. The injective case""; ""3.4. Injectives in the category of torsion Q[c[sub(H)]]-modules""; ""3.5. Proof of Theorem 3.1.1""; ""Chapter 4. Categorical reprocessing""; ""4.1. Recollections about derived categories""; ""4.2. Split linear triangulated categories""; ""4.3. The uniqueness theorem""; ""4.4. The algebraicization of the category of T-spectra over H""; ""4.5. The algebraicization of the category of F-spectra""; ""4.6. Euler classes revisited""; ""Chapter 5. Assembly and the standard model""""5.1. Assembly""; ""5.2. The ring t[sup(f)][sub(*)] ""; ""5.3. Global assembly""; ""5.4. The standard model category""; ""5.5. Homological algebra in the standard model""; ""5.6. The algebraicization of rational T-spectra""; ""5.7. Maps ; between injective spectra""; ""5.8. Algebraic cells and spheres""; ""5.9. Explicit models""; ""5.10. Hausdorff modules""; ""Chapter 6. The torsion model""; ""6.1. Practical calculations""; ""6.2. The torsion model""; ""6.3. Homological algebra in the torsion model""; ""6.4. The derived category of the torsion model""""6.5. Equivalence of derived categories of standard and torsion models""; ""6.6. Relationship to topology""; ""Part II. Change of groups functors in algebra and topology""; ""Chapter 7. Introduction to Part II""; ""7.1. General outline""; ""7.2. Modelling functors changing equivariance""; ""7.3. Functors between split triangulated categories""; ""Chapter 8. Induction, coinduction and geometric fixed points""; ""8.1. Forgetful, induction and coinduction functors""; ""8.2. The Lewis-May T-fixed point functor""; ""8.3. An algebraic model for geometric fixed points""""8.4. Analysis of geometric fixed points""; ""Chapter 9. Algebraic inflation and deflation""; ""9.1. Algebraic inflation and deflation of omitted f-modules""; ""9.2. Inflation and its right adjoint on the torsion model category""; ""Chapter 10. Inflation, Lewis-May fixed points and quotients""; ""10.1. The topological inflation and Lewis-May fixed point functors""; ""10.2. Inflation on objects""; ""10.3. Correspondence of Algebraic and geometric inflation functors""; ""10.4. A direct approach to the Lewis-May fixed point functor""; ""10.5. The homotopy type of Lewis-May fixed points""