**AMS Chelsea Publishing**

Volume: 347;
2004;
395 pp;
Hardcover

MSC: Primary 55;

Print ISBN: 978-0-8218-2967-7

Product Code: CHEL/347.H

List Price: $65.00

Individual Member Price: $58.50

**Electronic ISBN: 978-1-4704-2998-0
Product Code: CHEL/347.H.E**

List Price: $65.00

Individual Member Price: $58.50

# Complex Cobordism and Stable Homotopy Groups of Spheres: Second Edition

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*Douglas C. Ravenel*

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.

The book is intended for anyone wishing to study computational stable homotopy
theory. It is accessible to graduate students with a knowledge of algebraic
topology and recommended to anyone wishing to venture into the frontiers of the
subject.

#### Table of Contents

# Table of Contents

## Complex Cobordism and Stable Homotopy Groups of Spheres: Second Edition

- Cover Cover11
- Title page i2
- Dedication iii4
- Contents v6
- List of figures xi12
- List of tables xiii14
- Preface to the second edition xv16
- Preface to the first edition xvii18
- Commonly used notations xix20
- An introduction to the homotopy groups of spheres 122
- Setting up the Adams spectral sequence 4162
- The classical Adams spectral sequence 5980
- 𝐵𝑃-theory and the Adams-Novikov spectral sequence 103124
- The chromatic spectral sequence 147168
- Morava stabilizer algebras 187208
- Computing stable homotopy groups with the Adams-Novikov spectral sequence 225246
- Appendix A1. Hopf algebras and Hopf algebroids 299320
- Appendix A2. Formal group laws 339360
- Appendix A3. Tables of homotopy groups of spheres 361382
- Bibliography 377398
- Index 391412
- Back Cover Back Cover1418

#### Readership

Graduate students and research mathematicians interested in algebraic topology.

#### Reviews

This book on the Adams and Adams-Novikov spectral sequence and their applications to the computation of the stable homotopy groups of spheres is the first which does not only treat the definition and construction but leads the reader to concrete computations. It contains an overwhelming amount of material, examples, and machinery … The style of writing is very fluent, pleasant to read and typical for the author, as everyone who has read a paper written by him will recognize … this is a very welcome book …

-- Zentralblatt MATH

This book provides a substantial introduction to many of the current problems, techniques, and points of view in homotopy theory … gives a readable and extensive account of methods used to study the stable homotopy groups of spheres. It can be read by an advanced graduate student, but experts will also profit from it as a reference … fine exposition.

-- Mathematical Reviews