Nilpotence and periodicity in stable homotopy theory

also known as the orange book

Free download

As of March, 2015, it is also available for download here (hyperlinks added February, 2020 with further improvements in October, 2026).

Nilpotence and periodicity in stable homotopy theory (Annals of Mathematics Studies, No. 128), Princeton, NJ, 1992, xiv + 209 pp., $24.95. ISBN 0-691-02572-X. It is in print, and you can order it through Amazon books in paperback or hardback.

Amazon's description

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Published reviews

Corrections

If you find any misprints, please email them to me at dcravenel at gmail dot com; see also A note on the thick subcategory theorem (with A. Jeanneret and P. S. Landweber).