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Author : Dieter Degrijse
Publisher : American Mathematical Society
Page : 154 pages
File Size : 25,35 MB
Release : 2023-09-15
Category : Mathematics
ISBN : 1470467046
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Author : L. Gaunce Jr. Lewis
Publisher : Springer
Page : 548 pages
File Size : 16,62 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540470778
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Author : Michael A. Hill
Publisher : Cambridge University Press
Page : 881 pages
File Size : 20,47 MB
Release : 2021-07-29
Category : Mathematics
ISBN : 1108831443
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author : Stefan Schwede
Publisher : Cambridge University Press
Page : 847 pages
File Size : 27,13 MB
Release : 2018-09-06
Category : Mathematics
ISBN : 110842581X
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Author : J. Peter May
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 22,50 MB
Release : 1996
Category : Mathematics
ISBN : 0821803190
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Author : Dieter Degrijse
Publisher :
Page : 0 pages
File Size : 39,76 MB
Release : 2023
Category : Homotopy theory
ISBN : 9781470475741
Keywords: equivariant homotopy theory; proper action.
Author : Mark Hovey
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 29,60 MB
Release : 1997
Category : Mathematics
ISBN : 0821806246
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.
Author : Douglas C. Ravenel
Publisher : Princeton University Press
Page : 228 pages
File Size : 24,8 MB
Release : 1992-11-08
Category : Mathematics
ISBN : 9780691025728
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.
Author : Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 44,81 MB
Release : 2003-11-25
Category : Mathematics
ISBN : 082182967X
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.
Author : Glen E. Bredon
Publisher : Springer
Page : 72 pages
File Size : 25,96 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540349731
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