ABSTRACT
Equivariant orthogonal spectra and S-modules
by M.A. Mandell and J.P. May
The University of Chicago
mandell@math.uchicago.edu
may@math.uchicago.edu
April 20, 2000
subjclass: Primary 55P42, 55P43, 55P91;
Secondary 18A25, 18E30, 55P48, 55U35.
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.
\end{abstract}