nLab Complex cobordism and stable homotopy groups of spheres



Homological algebra

homological algebra

(also nonabelian homological algebra)



Basic definitions

Stable homotopy theory notions



diagram chasing

Schanuel's lemma

Homology theories


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


Chapter 1. An introduction to the Homotopy Groups of Spheres

1. Classical theorems Old and New

2. Methods of computing π *(S n)\pi_\ast(S^n)

3. The Adams-Novikov E 2E_2-term, Formal Group Laws, and the Greek Letter Construction

4. More formal group law theory, Morava’s point of view, and the Chromatic Spectral Sequence

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 ExtExt

5. Survey and further reading

Chapter 4. BPB P-Theory and the Adams-Novikov Spectral Sequence

1. Quillen’s theorem and the structure of BP (BP)BP_\bullet(BP)

2. A survey of BPB P-theory

3. Some calculations in BP (BP)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(BP /I n)Ext^1(B P_\bullet/I_n) and Hopf Invariant One

3. Ext(M 1)Ext(M^1) and the JJ-Homomorphism

4. Ext 2Ext^2 and the Thom Reduction

5. Periodic families in Ext 2Ext^2

6. Elements in Ext 3Ext^3 and Beyond

Chapter 6. Morava Stabilizer Algebras

1. The Change-of-Rings Isomorphism

2. The Structure of Σ(n)\Sigma(n)

3. The Cohomology of Σ(n)\Sigma(n)

4. The Odd Primary Kervaire Invariant Elements

5. The Spectra T(m)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 2. Formal Group Laws

Appendix 3. Table of homotopy groups of spheres

category: reference

Last revised on December 30, 2020 at 08:36:40. See the history of this page for a list of all contributions to it.