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Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May
| Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina | 514/.23 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0122-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Part I: General theory""; ""Â0. Preamble: definitions, change of universe, and split G-spectra""; ""Â1. Invariance properties of the functors f,c, and t""; ""Â2. Basic properties of the theories represented by f(k[sub(G)]), c(k[sub(G)]), and t(k[sub(G)])""; ""Â3. Homotopical behavior of the functors f,c, and t""; ""Â4. Completion at the augmentation ideal of the Burnside ring""; ""Â5. Transfer and the fixed point spectra of Tate G-spectra""; ""Part II: Eilenberg-Maclane G-spectra and the spectral sequences""
""Â6. Eilenberg-MacLane G-spectra and their associated theories""""Â7. Mackey functors and coefficient systems""; ""Â8. Products in the theories associated to Eilenberg-MacLane G-spectra""; ""Â9. Chain level calculation of the coefficient groups""; ""Â10. The f,c, and t Tate Atiyah-Hirzebruch spectral sequences""; ""Part III: Specializations and calculations""; ""Â11. Tate-Swan cohomology and the spectral sequences for finite groups""; ""Â12. Some remarks on nonequivariant stable homotopy theory""; ""Â13. The Tate K-theory of finite groups and related calculations"" ""Â14. Cyclic cohomology and the spectral sequences for the circle group""""Â15. Calculations in homotopy and K-theory for the circle group""; ""Â16. Free G-spheres and periodicity phenomena""; ""Part IV: The generalization to families""; ""Â17. Families and their f,c, and t G-spectra""; ""Â18. Cohomological and homological completion phenomena""; ""Â19. The generalized Tate G-spectra of periodic K-theory""; ""Â20. Theories associated to Mackey functors and coMackey functors""; ""Â21. Amitsur-Dress-Tate cohomology theories"" ""Â22. The generalized Tate Atiyah-Hirzebruch spectral sequences""""Â23. Some calculational methods and examples: groups of order pq""; ""Â24. Equivariant root invariants of stable homotopy groups of spheres""; ""Â25. Proof of the root invariant theorem""; ""Appendix A: Splittings of rational G-spectra for finite groups G""; ""Appendix B: Generalized Atiyah-Hirzebruch spectral sequences""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T""; ""U"" |
| Record Nr. | UNINA-9910480347903321 |
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May
| Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina | 514/.23 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homology theory |
| ISBN | 1-4704-0122-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Part I: General theory""; ""Â0. Preamble: definitions, change of universe, and split G-spectra""; ""Â1. Invariance properties of the functors f,c, and t""; ""Â2. Basic properties of the theories represented by f(k[sub(G)]), c(k[sub(G)]), and t(k[sub(G)])""; ""Â3. Homotopical behavior of the functors f,c, and t""; ""Â4. Completion at the augmentation ideal of the Burnside ring""; ""Â5. Transfer and the fixed point spectra of Tate G-spectra""; ""Part II: Eilenberg-Maclane G-spectra and the spectral sequences""
""Â6. Eilenberg-MacLane G-spectra and their associated theories""""Â7. Mackey functors and coefficient systems""; ""Â8. Products in the theories associated to Eilenberg-MacLane G-spectra""; ""Â9. Chain level calculation of the coefficient groups""; ""Â10. The f,c, and t Tate Atiyah-Hirzebruch spectral sequences""; ""Part III: Specializations and calculations""; ""Â11. Tate-Swan cohomology and the spectral sequences for finite groups""; ""Â12. Some remarks on nonequivariant stable homotopy theory""; ""Â13. The Tate K-theory of finite groups and related calculations"" ""Â14. Cyclic cohomology and the spectral sequences for the circle group""""Â15. Calculations in homotopy and K-theory for the circle group""; ""Â16. Free G-spheres and periodicity phenomena""; ""Part IV: The generalization to families""; ""Â17. Families and their f,c, and t G-spectra""; ""Â18. Cohomological and homological completion phenomena""; ""Â19. The generalized Tate G-spectra of periodic K-theory""; ""Â20. Theories associated to Mackey functors and coMackey functors""; ""Â21. Amitsur-Dress-Tate cohomology theories"" ""Â22. The generalized Tate Atiyah-Hirzebruch spectral sequences""""Â23. Some calculational methods and examples: groups of order pq""; ""Â24. Equivariant root invariants of stable homotopy groups of spheres""; ""Â25. Proof of the root invariant theorem""; ""Appendix A: Splittings of rational G-spectra for finite groups G""; ""Appendix B: Generalized Atiyah-Hirzebruch spectral sequences""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T""; ""U"" |
| Record Nr. | UNINA-9910788756203321 |
|
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May
| Generalized Tate cohomology / / J. P. C. Greenlees, J. P. May |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 |
| Descrizione fisica | 1 online resource (193 p.) |
| Disciplina | 514/.23 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homology theory |
| ISBN | 1-4704-0122-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Part I: General theory""; ""Â0. Preamble: definitions, change of universe, and split G-spectra""; ""Â1. Invariance properties of the functors f,c, and t""; ""Â2. Basic properties of the theories represented by f(k[sub(G)]), c(k[sub(G)]), and t(k[sub(G)])""; ""Â3. Homotopical behavior of the functors f,c, and t""; ""Â4. Completion at the augmentation ideal of the Burnside ring""; ""Â5. Transfer and the fixed point spectra of Tate G-spectra""; ""Part II: Eilenberg-Maclane G-spectra and the spectral sequences""
""Â6. Eilenberg-MacLane G-spectra and their associated theories""""Â7. Mackey functors and coefficient systems""; ""Â8. Products in the theories associated to Eilenberg-MacLane G-spectra""; ""Â9. Chain level calculation of the coefficient groups""; ""Â10. The f,c, and t Tate Atiyah-Hirzebruch spectral sequences""; ""Part III: Specializations and calculations""; ""Â11. Tate-Swan cohomology and the spectral sequences for finite groups""; ""Â12. Some remarks on nonequivariant stable homotopy theory""; ""Â13. The Tate K-theory of finite groups and related calculations"" ""Â14. Cyclic cohomology and the spectral sequences for the circle group""""Â15. Calculations in homotopy and K-theory for the circle group""; ""Â16. Free G-spheres and periodicity phenomena""; ""Part IV: The generalization to families""; ""Â17. Families and their f,c, and t G-spectra""; ""Â18. Cohomological and homological completion phenomena""; ""Â19. The generalized Tate G-spectra of periodic K-theory""; ""Â20. Theories associated to Mackey functors and coMackey functors""; ""Â21. Amitsur-Dress-Tate cohomology theories"" ""Â22. The generalized Tate Atiyah-Hirzebruch spectral sequences""""Â23. Some calculational methods and examples: groups of order pq""; ""Â24. Equivariant root invariants of stable homotopy groups of spheres""; ""Â25. Proof of the root invariant theorem""; ""Appendix A: Splittings of rational G-spectra for finite groups G""; ""Appendix B: Generalized Atiyah-Hirzebruch spectral sequences""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T""; ""U"" |
| Record Nr. | UNINA-9910817229803321 |
|
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island, United States : , : American Mathematical Society, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees
| Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1999 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homotopy theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0250-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910481049303321 |
|
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees
| Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1999 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homotopy theory |
| ISBN | 1-4704-0250-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788737803321 |
|
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees
| Rational S1-equivariant stable homotopy theory / / J.P.C. Greenlees |
| Autore | Greenlees J. P. C (John Patrick Campbell), <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1999 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
510 s
514/.24 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Homotopy theory |
| ISBN | 1-4704-0250-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910818128703321 |
|
Greenlees J. P. C (John Patrick Campbell), <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||