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Equivariant Orthogonal Spectra and $S$-Modules
 
M. A. Mandell University of Chicago, Chicago, IL
J. P. May University of Chicago, Chicago, IL
Equivariant Orthogonal Spectra and S-Modules
eBook ISBN:  978-1-4704-0348-5
Product Code:  MEMO/159/755.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
Equivariant Orthogonal Spectra and S-Modules
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Equivariant Orthogonal Spectra and $S$-Modules
M. A. Mandell University of Chicago, Chicago, IL
J. P. May University of Chicago, Chicago, IL
eBook ISBN:  978-1-4704-0348-5
Product Code:  MEMO/159/755.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1592002; 108 pp
    MSC: 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 well-known 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 well-suited 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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1592002; 108 pp
MSC: 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 well-known 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 well-suited 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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