Introduction To Stable Homotopy Theory
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Foundations Of Stable Homotopy Theory
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Author : David Barnes
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26
Foundations Of Stable Homotopy Theory written by David Barnes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.
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.
Introduction To Stable Homotopy Theory
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Author : David Barnes
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26
Introduction To Stable Homotopy Theory written by David Barnes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.
A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.
Equivariant Stable Homotopy Theory
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Author : L. Gaunce Jr. Lewis
language : en
Publisher: Springer
Release Date : 2006-11-14
Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics 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.
Stable And Unstable Homotopy
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Author : William G. Dwyer
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-01-01
Stable And Unstable Homotopy written by William G. Dwyer 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 1998-01-01 with Mathematics categories.
This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during 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.
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.
Equivariant Homotopy And Cohomology Theory
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Equivariant Homotopy And Cohomology Theory written by J. Peter May 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 1996 with Science categories.
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 book 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. It 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. It introduces many of the fundamental ideas and concepts of modern algebraic topology. It presents comprehensive material not found in any other book on the subject. It provides a coherent overview of many areas of current interest in algebraic topology. It surveys a great deal of material, explaining main ideas without getting bogged down in details.
Introduction To Homotopy Theory
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Author : Paul Selick
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Introduction To Homotopy Theory written by Paul Selick 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 2008 with Mathematics categories.
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
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.
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem
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Author : Michael A. Hill
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-29
Equivariant Stable Homotopy Theory And The Kervaire Invariant Problem written by Michael A. Hill and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Mathematics categories.
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
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