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.
Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128
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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Arbeitsgemeinschaft Mit Aktuellem Thema: The Nilpotence Theorem in Stable Homotopy Theory
Arbeitsgemeinschaft Mit Aktuellem Thema: The 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 Arbeitsgemeinschaft Mit Aktuellem Thema: The Nilpotence Theorem in Stable Homotopy Theory write by . This book was released on 1998. Arbeitsgemeinschaft Mit Aktuellem Thema: The Nilpotence Theorem in Stable Homotopy Theory available in PDF, EPUB and Kindle.
Axiomatic Stable Homotopy Theory
Axiomatic 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 Axiomatic Stable Homotopy Theory write by Mark Hovey. This book was released on 1997. Axiomatic Stable Homotopy Theory available in PDF, EPUB and Kindle. We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.
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.
