Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 write by Douglas C. Ravenel. This book was released on 2016-03-02. Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 available in PDF, EPUB and Kindle. 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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Nilpotence and periodicity in Stable Homotopy Theory
Nilpotence and periodicity in Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nilpotence and periodicity in Stable Homotopy Theory write by Douglas C. Ravenel. This book was released on 1992. Nilpotence and periodicity in Stable Homotopy Theory available in PDF, EPUB and Kindle.
Complex Cobordism and Stable Homotopy Groups of Spheres
Complex Cobordism and Stable Homotopy Groups of Spheres - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Complex Cobordism and Stable Homotopy Groups of Spheres write by Douglas C. Ravenel. This book was released on 2003-11-25. Complex Cobordism and Stable Homotopy Groups of Spheres available in PDF, EPUB and Kindle. 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 on the stable 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.
A Nilpotence Theorem in Stable Homotopy Theory
A Nilpotence Theorem in Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Nilpotence Theorem in Stable Homotopy Theory write by Ethan Sander Devinatz. This book was released on 1985. A Nilpotence Theorem in Stable Homotopy Theory available in PDF, EPUB and Kindle.
Foundations of Stable Homotopy Theory
Foundations of Stable Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Stable Homotopy Theory write by David Barnes. This book was released on 2020-03-26. Foundations of Stable Homotopy Theory available in PDF, EPUB and Kindle. 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 much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
