Proper Equivariant Stable Homotopy Theory
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Proper Equivariant Stable Homotopy Theory
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Author : Dieter Degrijse
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-15
Proper Equivariant Stable Homotopy Theory written by Dieter Degrijse 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 2023-09-15 with Mathematics categories.
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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.
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 Mathematics 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 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.
Equivariant Stable Homotopy Theory
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Author : L. Gaunce Jr. Lewis
language : en
Publisher:
Release Date : 2014-01-15
Equivariant Stable Homotopy Theory written by L. Gaunce Jr. Lewis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Equivariant Homotopy And Cohomology Theory
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Author : J. Peter May
language : en
Publisher:
Release Date : 1996
Equivariant Homotopy And Cohomology Theory written by J. Peter May and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Homology theory 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. T.
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.
Global Homotopy Theory
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Author : Stefan Schwede
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-06
Global Homotopy Theory written by Stefan Schwede 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 2018-09-06 with Mathematics categories.
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Rational S 1 Equivariant Stable Homotopy Theory
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Author : John Patrick Campbell Greenlees
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Rational S 1 Equivariant Stable Homotopy Theory written by John Patrick Campbell Greenlees 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 1999 with Mathematics categories.
The memoir presents a systematic study of rational S1-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.
Parametrized Homotopy Theory
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Parametrized Homotopy 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 2006 with Mathematics categories.
This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.
Rings Modules And Algebras In Stable Homotopy Theory
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Author : Anthony D. Elmendorf
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Rings Modules And Algebras In Stable Homotopy Theory written by Anthony D. Elmendorf 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 introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a