دانلود کتاب The Adams spectral sequence for topological modular forms

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Contents List of Figures List of Tables Preface Introduction 0.1. Topological modular forms 0.2. (Co-)homology and complex bordism of ??? 0.3. The Adams ?₂-term for ? 0.4. The Adams differentials for ? 0.5. The Adams ?₂-term for ??? 0.6. The Adams differentials for ??? 0.7. The graded homotopy ring of ??? 0.8. Duality 0.9. The sphere spectrum 0.10. Finite coefficients 0.11. Odd primes 0.12. Adams charts Part 1. The Adams ?₂-term Chapter 1. Minimal resolutions 1.1. The Adams ?₂-term for ? 1.2. The Adams ?₂-term for ??? 1.3. Steenrod operations in ?₂(???) 1.4. The Adams ?₂-term for ???/2, ???/? and \tmf/? Chapter 2. The Davis–Mahowald spectral sequence 2.1. ??? over a pair of Hopf algebras 2.2. A dual formulation 2.3. A filtered cobar complex 2.4. Multiplicative structure 2.5. The spectral sequence for ?(1) 2.6. Real, quaternionic and complex ?-theory spectra Chapter 3. ??? over ?(2) 3.1. The Davis–Mahowald ?₁-term for ?(2) 3.2. Syzygies and Adams covers 3.3. A comparison of ?(1)_{*}-comodule algebras 3.4. The ?₁-differential for ?(2) 3.5. The Shimada–Iwai presentation Chapter 4. ??? with coefficients 4.1. Coefficients in ?₁ 4.2. Adams periodicity 4.3. Coefficients in ?₂ 4.4. Coefficients in ?₄ Part 2. The Adams differentials Chapter 5. The Adams spectral sequence for ??? 5.1. The ?₂-term for ??? 5.2. The ?₂-differentials for ??? 5.3. The ?₃-differentials for ??? 5.4. The ?₄-differentials for ??? 5.5. The ?_{∞}-term for ??? Chapter 6. The Adams spectral sequence for ???/2 6.1. The ?₂-term for ???/2 6.2. The ?₂-differentials for ???/2 6.3. The ?₃-differentials for ???/2 6.4. The ?₄-differentials for ???/2 6.5. The ?_{∞}-term for ???/2 Chapter 7. The Adams spectral sequence for ???/? 7.1. The ?₂-term for ???/? 7.2. The ?₂-differentials for ???/? 7.3. The ?₃-differentials for ???/? 7.4. The ?_{∞}-term for ???/? Chapter 8. The Adams spectral sequence for ???/? 8.1. The ?₂-term for ???/? 8.2. The ?₂-differentials for ???/? 8.3. The ?₃-differentials for ???/? 8.4. The ?₄-differentials for ???/? 8.5. The ?_{∞}-term for ???/? Part 3. The abutment Chapter 9. The homotopy groups of ??? 9.1. Algebra generators for the ?_{∞}-term 9.2. Hidden extensions 9.3. The image of ?_{*}(???) in modular forms 9.4. Algebra generators for ?_{*}(???) 9.5. Relations in ?_{*}(???) 9.6. The algebra structure of ?_{*}(???) Chapter 10. Duality 10.1. Pontryagin duality in the ?-power torsion of ?_{*}(???) 10.2. Torsion submodules and divisible quotients 10.3. Brown–Comenetz duality 10.4. Anderson duality 10.5. Explicit formulas Chapter 11. The Adams spectral sequence for the sphere 11.1. ?_{∞} ring spectra 11.2. Steenrod operations in ?₂(?) 11.3. The Adams ?- and ?-invariants 11.4. Some ?₂-differentials for ? 11.5. Some ?₃-differentials for ? 11.6. Some ?₄-differentials for ? 11.7. Collapse at ?₅ 11.8. Some homotopy groups of ? 11.9. A hidden ?-extension 11.10. The ???-Hurewicz homomorphism 11.11. The ???-Hurewicz image Chapter 12. Homotopy of some finite cell ???-modules 12.1. Homotopy of ???/2 12.2. Homotopy of ???/? 12.3. Homotopy of ???/? 12.4. Homotopy of ???/? 12.5. Homotopy of ???/(2,?) 12.6. Modified Adams spectral sequences Chapter 13. Odd primes 13.1. The ???-module Steenrod algebra and its dual 13.2. The Adams ?₂-term 13.3. The Adams differentials 13.4. The graded ring ?_{*}(???) 13.5. Brown–Comenetz and Anderson duality 13.6. Explicit formulas 13.7. The ???-Hurewicz image Appendix A. Calculation of ?ᵣ(???) for ?=3,4,5 A.1. Calculation of ?₃(???)=?(?₂(???),?₂) A.2. Calculation of ?₄(???)=?(?₃(???),?₃) A.3. Calculation of ?₅(???)=?(?₄(???),?₄) Appendix B. Calculation of ?ᵣ(???/2) for ?=3,4,5 B.1. Calculation of ?₃(???/2)=?(?₂(???/2),?₂) B.2. Calculation of ?₄(???/2)=?(?₃(???/2),?₃) B.3. Calculation of ?₅(???/2)=?(?₄(???/2),?₄) Appendix C. Calculation of ?ᵣ(???/?) for ?=3,4 C.1. Calculation of ?₃(???/?)=?(?₂(???/?),?₂) C.2. Calculation of ?₄(???/?)=?(?₃(???/?),?₃) Appendix D. Calculation of ?ᵣ(???/?) for ?=3,4,5 D.1. Calculation of ?₃(???/?)=?(?₂(???/?),?₂) D.2. Calculation of ?₄(???/?)=?(?₃(???/?),?₃) D.3. Calculation of ?₅(???/?)=?(?₄(???/?),?₄) Bibliography Index