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

Released on by Douglas C. Ravenel
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  • Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 Book Detail

  • Author : Douglas C. Ravenel
  • Release Date : 2016-03-02
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 224
  • ISBN 13 : 1400882486
  • File Size : 90,90 MB
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Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 by Douglas C. Ravenel PDF Summary

Book 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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

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Foundations of Stable Homotopy Theory

Foundations of Stable Homotopy Theory

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The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is