Equivariant Homotopy And Cohomology Theory
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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 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 Homotopy And Cohomology Theory
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Author : M. Cole
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-01-01
Equivariant Homotopy And Cohomology Theory written by M. Cole 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 1996-01-01 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 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 Cohomology Theories
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Author : Glen E. Bredon
language : en
Publisher: Springer
Release Date : 2006-11-14
Equivariant Cohomology Theories written by Glen E. Bredon 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.
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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.
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 Ordinary Homology And Cohomology
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Author : Steven R. Costenoble
language : en
Publisher: Springer
Release Date : 2017-01-02
Equivariant Ordinary Homology And Cohomology written by Steven R. Costenoble and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-02 with Mathematics categories.
Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions.
Diagram Cohomology And Isovariant Homotopy Theory
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Author : Giora Dula
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Diagram Cohomology And Isovariant Homotopy Theory written by Giora Dula 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 1994 with Mathematics categories.
Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.
Fixed Point Theory Of Parametrized Equivariant Maps
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Author : Hanno Ulrich
language : en
Publisher: Springer
Release Date : 2006-11-15
Fixed Point Theory Of Parametrized Equivariant Maps written by Hanno Ulrich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. It thus addresses equivariant point set topology as well as equivariant homotopy theory. Notable tools are vertical Jaworowski criterion and an equivariant transversality theorem. The second part presents equivariant cohomology theory showing that equivariant fixed point theory is isomorphic to equivariant stable cohomotopy theory. A crucial result is the sum decomposition of the equivariant fixed point index which provides an insight into the structure of the theory's coefficient group. Among the consequences of the sum formula are some Borsuk-Ulam theorems as well as some folklore results on compact Lie-groups. The final section investigates the fixed point index in equivariant K-theory. The book is intended to be a thorough and comprehensive presentation of its subject. The reader should be familiar with the basics of the theory of compact transformation groups. Good knowledge of algebraic topology - both homotopy and homology theory - is assumed. For the advanced reader, the book may serve as a base for further research. The student will be introduced into equivariant fixed point theory; he may find it helpful for further orientation.
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.