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OverviewThe 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. Full Product DetailsAuthor: M.A. Mandall , J.Peter MayPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated Edition Volume: No. 159 Weight: 0.255kg ISBN: 9780821829363ISBN 10: 082182936 Pages: 108 Publication Date: 30 August 2002 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. 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."ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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