Memoirs of the American Mathematical Society 2002; 108 pp; softcover Volume: 159 ISBN10: 082182936X ISBN13: 9780821829363 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/159/755
 The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most wellknown examples are the category of \(S\)modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of \(S\)modules and symmetric spectra and which is particularly wellsuited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to \(S\)modules. We then develop the equivariant theory. For a compact Lie group \(G\), we construct a symmetric monoidal model category of orthogonal \(G\)spectra whose homotopy category is equivalent to the classical stable homotopy category of \(G\)spectra. We also complete the theory of \(S_G\)modules and compare the categories of orthogonal \(G\)spectra and \(S_G\)modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory. Readership Graduate students and research mathematicians interested in algebraic topology. Table of Contents  Introduction
 Orthogonal spectra and \(S\)modules
 Equivariant orthogonal spectra
 Model categories of orthogonal \(G\)spectra
 Orthogonal \(G\)spectra and \(S_G\)modules
 "Change" functors for orthogonal \(G\)spectra
 "Change" functors for \(S_G\)modules and comparisons
 Bibliography
 Index of notation
