eBook ISBN:  9781470403485 
Product Code:  MEMO/159/755.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 
eBook ISBN:  9781470403485 
Product Code:  MEMO/159/755.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 159; 2002; 108 ppMSC: Primary 55; Secondary 18
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.
ReadershipGraduate students and research mathematicians interested in algebraic topology.

Table of Contents

Chapters

Introduction

I. Orthogonal spectra and $S$modules

II. Equivariant orthogonal spectra

III. Model categories of orthogonal $G$spectra

IV. Orthogonal $G$spectra and $S_G$modules

V. “Change” functors for orthogonal $G$spectra

VI. “Change” functors for $S_G$modules and comparisons


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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.
Graduate students and research mathematicians interested in algebraic topology.

Chapters

Introduction

I. Orthogonal spectra and $S$modules

II. Equivariant orthogonal spectra

III. Model categories of orthogonal $G$spectra

IV. Orthogonal $G$spectra and $S_G$modules

V. “Change” functors for orthogonal $G$spectra

VI. “Change” functors for $S_G$modules and comparisons