Complex Cobordism And Stable Homotopy Groups Of Spheres (Ams Chelsea Publishing)

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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 ...

Series: AMS Chelsea Publishing
Hardcover: 395 pages
Publisher: American Mathematical Society; 2 edition (November 25, 2003)
Language: English
ISBN-10: 082182967X
ISBN-13: 978-0821829677
Product Dimensions: 7.2 x 1 x 10.2 inches
Amazon Rank: 2683854
Format: PDF ePub Text djvu ebook

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The author is a real expert. Detailed computations cannot be found in any other books. This is a book that every algebraic topologist must have....

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le 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.