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Complex cobordism and stable homotopy groups of spheres
Context
Homological algebra
Stable Homotopy theory
This entry collects pointers related to the book
on stable homotopy theory in general and in particular the computation of the homotopy groups of spheres via the Adams-Novikov spectral sequence and its use of complex cobordism cohomology theory .
My initial inclination was to call this book The Music of the Spheres , but I was dissuaded from doing so by my diligent publisher, who is ever mindful of the sensibilities of librarians. (preface to the first edition)
See also
Contents
Chapter 1. An introduction to the Homotopy Groups of Spheres
1. Classical theorems Old and New
2. Methods of computing $\pi_\ast(S^n)$
5. Unstable homotopy groups and the EHP spectral sequence
Chapter 2. Setting up the Adams Spectral sequence
1. The classical Adams spectral sequence
2. The Adams spectral sequence based on a generalized homology theory
3. The smash product pairing and the Generalized connecting homomorphism
Chapter 3. The Classical Adams Spectral Sequence
1. The Steenrod algebra and some easy calculuation
2. The May spectral sequence
3. The Lambda Algebra
4. Some general properties of $Ext$
5. Survey and further reading
Chapter 4. $B P$ -Theory and the Adams-Novikov Spectral Sequence
1. Quillen’s theorem and the structure of $BP_\bullet(BP)$
2. A survey of $B P$ -theory
3. Some calculations in $B P_\bullet(B P)$
4. Beginning calculations with the Adams-Novikov Spectral Sequence
Chapter 5. The Chromatic Spectral Sequence
1. The algebraic construction
2. $Ext^1(B P_\bullet/I_n)$ and Hopf Invariant One
3. $Ext(M^1)$ and the $J$ -Homomorphism
4. $Ext^2$ and the Thom Reduction
5. Periodic families in $Ext^2$
6. Elements in $Ext^3$ and Beyond
Chapter 6. Morava Stabilizer Algebras
1. The Change-of-Rings Isomorphism
2. The Structure of $\Sigma(n)$
3. The Cohomology of $\Sigma(n)$
4. The Odd Primary Kervaire Invariant Elements
5. The Spectra $T(m)$
Chapter 7. Computing Stable Homotopy Groups with the Adams-Novikov Spectral Sequence
Appendix 1. Hopf Algebras and Hopf Algebroids
1. Basic definitions
2. Homological algebra
3. Some spectral sequences
4. Massey products
5. Algebraic Steenrod operations
Appendix 3. Table of homotopy groups of spheres