Rational S 1 Equivariant Stable Homotopy Theory

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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.

Rational S1 Equivariant Stable Homotopy Theory

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Author : J. P. C. Greenlees
language : it
Publisher:
Release Date : 1999

Rational S1 Equivariant Stable Homotopy Theory written by J. P. C. Greenlees and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Equivariant Topology And Derived Algebra

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Author : Scott Balchin
language : en
Publisher: Cambridge University Press
Release Date : 2022

Equivariant Topology And Derived Algebra written by Scott Balchin 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 2022 with Mathematics categories.

A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

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.

Rational Homotopical Models And Uniqueness

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Author : Martin Majewski
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Rational Homotopical Models And Uniqueness written by Martin Majewski 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 2000 with Mathematics categories.

The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.

Equivariant E Theory For C Algebras

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Author : Erik Guentner
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Equivariant E Theory For C Algebras written by Erik Guentner 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 2000 with Mathematics categories.

This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space

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.

An Alpine Expedition Through Algebraic Topology

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Author : Christian Ausoni
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-09

An Alpine Expedition Through Algebraic Topology written by Christian Ausoni 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 2014-06-09 with Mathematics categories.

This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.

Splitting Theorems For Certain Equivariant Spectra

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Author : L. Gaunce Lewis
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Splitting Theorems For Certain Equivariant Spectra written by L. Gaunce Lewis 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 2000 with Mathematics categories.

This book is intended for graduate students and research mathematicians interested in algebraic topology.

An Alpine Anthology Of Homotopy Theory

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Author : Dominique Arlettaz
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

An Alpine Anthology Of Homotopy Theory written by Dominique Arlettaz 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.

The second Arolla conference on algebraic topology brought together specialists covering a wide range of homotopy theory and $K$-theory. These proceedings reflect both the variety of talks given at the conference and the diversity of promising research directions in homotopy theory. The articles contained in this volume include significant contributions to classical unstable homotopy theory, model category theory, equivariant homotopy theory, and the homotopy theory of fusionsystems, as well as to $K$-theory of both local fields and $C*$-algebras.