Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 / Douglas C. Ravenel.

Format:

Book

Author/Creator:

Ravenel, Douglas C., author.

Series:

Annals of mathematics studies ; no. 128.

Annals of Mathematics Studies ; 310

Language:

English

Subjects (All):

Homotopy theory.

Physical Description:

1 online resource (225 pages)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Contents:

Frontmatter

Contents

Preface

Introduction

Chapter 1. The main theorems

Chapter 2. Homotopy groups and the chromatic filtration

Chapter 3. MU-theory and formal group laws

Chapter 4. Morava's orbit picture and Morava stabilizer groups

Chapter 5. The thick subcategory theorem

Chapter 6. The periodicity theorem

Chapter 7. Bousfield localization and equivalence

Chapter 8. The proofs of the localization, smash product and chromatic convergence theorems

Chapter 9. The proof of the nilpotence theorem

Appendix A. Some tools from homotopy theory

Appendix B. Complex bordism and BP-theory

Appendix C. Some idempotents associated with the symmetric group

Bibliography

Index

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882489

1400882486

OCLC:

979911360