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Equivariant stable homotopy theory

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Published by Springer-Verlag in Berlin, New York .
Written in English

Subjects:

  • Homotopy theory.

Book details:

Edition Notes

StatementL.G. Lewis, Jr., J.P. May, M. Steinberger.
SeriesLecture notes in mathematics ;, 1213, Lecture notes in mathematics (Springer-Verlag) ;, 1213.
ContributionsMay, J. Peter., Steinberger, M. 1950-
Classifications
LC ClassificationsQA3 .L28 no. 1213, QA612.7 .L28 no. 1213
The Physical Object
Paginationix, 538 p. :
Number of Pages538
ID Numbers
Open LibraryOL2731852M
ISBN 100387168206
LC Control Number86025968

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1. Equivariant homotopy We shall not give a systematic exposition of equivariant homotopy theory. There are several good books on the subject, such as [12] and [17], and a much more thor-ough expository account will be given in [53]. Some other expository articles are [49, 1]. We aim merely to introduce ideas, fix notations, and establish. Get this from a library! Equivariant stable homotopy theory. [L G Lewis; J Peter May; M Steinberger] -- 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. We review some foundations for equivariant stable homotopy theory in the context of orthogonal G-spectra. The main reference for this theory is the AMS memoir [16] by Mandell and May; the appendices of the paper [10] by Hill, Hopkins and Ravenel contain further material, in .   Using these structure theorems and a technique with the flag variety dating back to Quillen, we then show that large classes of equivariant cohomology theories for which a type of complex-orientability holds are nilpotent for the family of abelian subgroups.

A SURVEY OF EQUIVARIANT STABLE HOMOTOPY THEORY GUNNAR CARLSSON~ (Receiced 15 March ; in revised firm I2 October ) INTRODUCTION EQUIVARIANT stable homotopy theory was invented by G. B. Segal in the early s [45]. He was motivated by his work with Atiyah [9] on equivariant K-theory, generalizing an. Equivariant Stable Homotopy Theory Notes. This repository holds lecture notes for Andrew Blumberg's class on equivariant homotopy theory at UT Austin in Spring This repo holds the source code, ,.bib, files; the compiled PDF is available here.. These notes were live-TeXed each day in class, then edited afterwards to correct typos, add references, etc. would like to say a few words on equivariant stable homotopy theory. The G-equivariant stable homotopy category (indexed on a complete G-universe), for any compact Lie group G, was introduced in the book [LMSM86]. Roughly speaking, the 5. objects of this category are G-spectra indexed on nite dimensional G-representations. SLN Equivariant stable homotopy theory (with Lewis, Steinberger, and with contributions by McClure) A brief guide to some addenda and errata (pdf) American Mathematical Society Memoirs and Asterisque (at AMS) Memoirs On the Theory and Applications of Torsion Products (with Gugenheim) ($11).

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. stable homotopy theory by reading Lewis-May-Steinberger’s book [LMS86] on equivariant stable homotopy theory and letting G =, but this may not appeal to everyone. In any case, perhaps this isn’t necessarily a good reference for nontrivial groups. Unstable equivariant questions are very natural, and somewhat reasonable. Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem-Michael A. Hill The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the s and was quickly recognised as one of the most important problems in the field.   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.