Ravenel, Douglas C.
Complex cobordism and stable homotopy groups of spheres : 2 nd ed. - 2 ed. - USA: AMS, [c2004] - 395 p
Chapter 1. An introduction to the homotopy groups of spheres
Chapter 2. Setting up the Adams spectral sequence
Chapter 3. The classical Adams spectral sequence
Chapter 4. BP-theory and the Adams-Novikov spectral sequence
Chapter 5. The chromatic spectral sequence
Chapter 6. Morava stabilizer algebras
Chapter 7. Computing stable homotopy groups with the Adams-Novikov spectral sequence
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres.
The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids.
9780821829677
QA3
Complex cobordism and stable homotopy groups of spheres : 2 nd ed. - 2 ed. - USA: AMS, [c2004] - 395 p
Chapter 1. An introduction to the homotopy groups of spheres
Chapter 2. Setting up the Adams spectral sequence
Chapter 3. The classical Adams spectral sequence
Chapter 4. BP-theory and the Adams-Novikov spectral sequence
Chapter 5. The chromatic spectral sequence
Chapter 6. Morava stabilizer algebras
Chapter 7. Computing stable homotopy groups with the Adams-Novikov spectral sequence
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres.
The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids.
9780821829677
QA3