Stable Homotopy And Generalised Homology
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Stable Homotopy And Generalised Homology
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Author : John Frank Adams
language : en
Publisher: University of Chicago Press
Release Date : 1974
Stable Homotopy And Generalised Homology written by John Frank Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Stable Homotopy And Generalized Homology
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Author : John Frank Adams
language : en
Publisher:
Release Date : 1974
Stable Homotopy And Generalized Homology written by John Frank Adams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Homology theory categories.
Complex Cobordism And Stable Homotopy Groups Of Spheres
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Author :
language : en
Publisher: Academic Press
Release Date : 1986-05-05
Complex Cobordism And Stable Homotopy Groups Of Spheres written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-05 with Mathematics categories.
Complex Cobordism and Stable Homotopy Groups of Spheres
Equivariant Stable Homotopy Theory
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Author : L. Gaunce Lewis (jr.)
language : en
Publisher: Springer
Release Date : 1986
Equivariant Stable Homotopy Theory written by L. Gaunce Lewis (jr.) and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Homology theory categories.
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.
Nilpotence And Periodicity In Stable Homotopy Theory
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Author : Douglas C. Ravenel
language : en
Publisher: Princeton University Press
Release Date : 1992-11-08
Nilpotence And Periodicity In Stable Homotopy Theory written by Douglas C. Ravenel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-08 with Mathematics categories.
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.
Algebraic Topology Homotopy And Homology
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Author : Robert M. Switzer
language : en
Publisher: Springer
Release Date : 1975
Algebraic Topology Homotopy And Homology written by Robert M. Switzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. After an account of classical homotopy theory, the author turns to homology and cohomology theories, first treating them axiomatically and then constructing them using spectra. These ideas are illustrated via a thorough development of the three main examples of ordinary homology, K-theory and bordisms. Next, the author takes up the study of products in homology and cohomology and the related questions of orientability and duality. The remainder of the book is devoted to more sophisticated techniques and methods currently in use such as characteristic classes, cohomology operations, and the Adams spectral sequence, all of which are developed in the context of generalized homology theories. This book is, all in all, a very admirable work and a valuable addition to the literature and its value is not diminished by the somewhat minor flaws mentioned. -- S.Y. Husseini.
Complex Cobordism And Stable Homotopy Groups Of Spheres
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Author : Douglas C. Ravenel
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-09
Complex Cobordism And Stable Homotopy Groups Of Spheres written by Douglas C. Ravenel and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Mathematics categories.
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
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Author : John Harold Palmieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Stable Homotopy Over The Steenrod Algebra written by John Harold Palmieri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Homotopy theory categories.
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
Axiomatic Stable Homotopy Theory
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Author : Mark Hovey
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Axiomatic Stable Homotopy Theory written by Mark Hovey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This book gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a 'stable homotopy category'; using these axioms, one can make various constructions - cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories. Next, a number of examples of such categories are presented. Some of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). Hence one can apply many of the tools of stable homotopy theory to these algebraic situations.This work: provides a reference for standard results and constructions in stable homotopy theory; discusses applications of those results to algebraic settings, such as group theory and commutative algebra; provides a unified treatment of several different situations in stable homotopy, including equivariant stable homotopy and localizations of the stable homotopy category; and, also provides a context for nilpotence and thick subcategory theorems, such as the nilpotence theorem of Devinatz-Hopkins-Smith and the thick subcategory theorem of Hopkins-Smith in stable homotopy theory, and the thick subcategory theorem of Benson-Carlson-Rickard in representation theory. This book presents stable homotopy theory as a branch of mathematics in its own right with applications in other fields of mathematics. It is a first step toward making stable homotopy theory a tool useful in many disciplines of mathematics.
Algebraic Topology Homotopy And Homology
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Author : Robert M. Switzer
language : en
Publisher: Springer
Release Date : 2017-12-01
Algebraic Topology Homotopy And Homology written by Robert M. Switzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-01 with Mathematics categories.
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews