Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128

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.\n\nDuring 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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group. Additional ISBNs 069102572X, 9780691025728Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 is written by Douglas C. Ravenel and published by Princeton University Press. ISBNs for Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 are 9781400882489, 1400882486 and the print ISBNs are 9780691087924, 069108792X. Additional ISBNs include 069102572X, 9780691025728.