Author: Ethan Sander DevinatzPublisher:
ISBN:
Category :
Languages : en
Pages : 170
Book Description
A Nilpotence Theorem in Stable Homotopy Theory
Author: Ethan Sander DevinatzPublisher:
ISBN:
Category :
Languages : en
Pages : 170
Book Description
Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128
Author: Douglas C. RavenelPublisher: Princeton University Press
ISBN: 1400882486
Category : Mathematics
Languages : en
Pages : 224
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 It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Arbeitsgemeinschaft Mit Aktuellem Thema: The Nilpotence Theorem in Stable Homotopy Theory
Author: Axiomatic Stable Homotopy Theory
Author: Mark HoveyPublisher: American Mathematical Soc.
ISBN: 0821806246
Category : Mathematics
Languages : en
Pages : 130
Book Description
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.
Nilpotence and periodicity in Stable Homotopy Theory
Author: Douglas C. RavenelComplex Cobordism and Stable Homotopy Groups of Spheres
Author: Douglas C. RavenelPublisher: American Mathematical Soc.
ISBN: 082182967X
Category : Mathematics
Languages : en
Pages : 418
Book Description
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.
Stable Homotopy over the Steenrod Algebra
Author: John Harold PalmieriPublisher: American Mathematical Soc.
ISBN: 0821826689
Category : Mathematics
Languages : en
Pages : 193
Book Description
This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu
Stable and Unstable Homotopy
Author: William G. DwyerPublisher: American Mathematical Soc.
ISBN: 0821808249
Category : Mathematics
Languages : en
Pages : 326
Book Description
This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Field Institute as part of the homotopy program for the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
Odd Primary Infinite Families in Stable Homotopy Theory
Author: Ralph L. CohenPublisher: American Mathematical Soc.
ISBN: 082182242X
Category : Adams spectral sequences
Languages : en
Pages : 102
Book Description
Addresses issues with odd primary infinite families in stable homotopy theory.
Stable Homotopy Theory
Author: J.F. AdamsPublisher: Springer
ISBN: 3662159058
Category : Mathematics
Languages : en
Pages : 84
Book Description