Title:
Stabilization as a CW approximation
Author:
A. D. Elmendorf
aelmendo@math.purdue.edu
Department of Mathematics
Purdue University Calumet
Hammond, IN 46323
AMS classification number:
55P42
This is a revised version of a paper previously posted to the archive.
The results are all the same, but the proofs have been extensively
revised, in the hope of improving their comprehensibility.
The previous abstract reads:
This paper describes a peculiar property of the category of
$S$-modules constructed by the author, Kriz, Mandell, and May: the full
subcategory of suspension spectra (which are all $S$-modules) forms a
precise copy of the category of topological spaces. Consequently, the
``classical'' homotopy category of $S$-modules with morphisms the actual
homotopy classes of maps contains a copy of unstable homotopy theory.
Stabilization and stable homotopy are then induced by CW approximation as
$S$-modules. One consequence is that CW complexes whose suspension spectra
are CW $S$-modules must be contractible.