Equivariant Stable Homotopy Theory
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L. G. Lewis, Jr. J.P May M. Steinberger with contributions by J. E. McClure
Equivariant Stable Homotopy Theory
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Authors
L. Gaunce Lewis, Jr. Syracuse University, Syracuse, New York 13244, USA
J. Peter May University of Chicago, Chicago, Illinois 60637, USA Mark Steinberger Rutgers University, Newark, New Jersey 07102, USA
Mathematics Subject Classification (1980): 55-02, 55M05, 55M35, 55N20, 55N25, 55P25, 55P42,57S99 ISBN 3-540-16820-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387 -16820-6 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Preface Our primary purpose in this volume is to establish the fmmdations of
equivariant stable homotopy theory.
To this end, we shall construct a stable
homotopy category of G-spectra enjoying all of the good properties one might reasonably expect, where
G is a compact Lie group.
We shall use this category to
study equivariant duality, equivariant transfer, the Burnside ring, and related topics in equivariant homology and cohomology theory. This volume originated as a sequel to the volume applications" in this series [20].
"H", ring spectra and their
However, our goals changed as work progressed,
and most of this volume is now wholly independent of [20J.
In fact, we have two On the one hand, we are interested in equivariant homotopy theory, the algebraic topology of spaces with group actions, as a fascinating subject of study in its own right. On the other hand, we are interested in equivariant homotopy theory as a tool for obtaining useful information in classical nonequivariant homotopy theory. This division of motivation is reflected in a division of material into two halves. The first half, chapters I-V, is primarily addressed to the reader interested in equivariant theory. The second half, chapters VI-X, is primarily addressed to the reader interested in nonequivariant applications. It gives the construction and analysis of extended powers of spectra that served as the starting point for [20J. It also gives a systematic study of generalized Thom spectra. With a very few minor and peripheral exceptions, the second half depends only on chapter I and the first four sections of chapter II from the first half. The reader is referred to [105] for a very brief guided tour of some of the high spots of the second half.
essentially disjoint motives for undertaking this study.
Chapter I gives the more elementary features of the equivariant
