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