The Adams spectral sequence for topological modular forms

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