Geometry & Topology

On the homotopy groups of symmetric spectra

Stefan Schwede

Abstract

We construct a natural, tame action of the monoid of injective self-maps of the set of natural numbers on the homotopy groups of a symmetric spectrum. This extra algebraic structure allows a conceptual and uniform understanding of various phenomena related to $π∗$–isomorphisms, semistability and the relationship between naive and true homotopy groups for symmetric spectra.

Article information

Source
Geom. Topol., Volume 12, Number 3 (2008), 1313-1344.

Dates
Received: 30 September 2006
Accepted: 5 April 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800098

Digital Object Identifier
doi:10.2140/gt.2008.12.1313

Mathematical Reviews number (MathSciNet)
MR2421129

Zentralblatt MATH identifier
1146.55005

Subjects
Primary: 55P42: Stable homotopy theory, spectra
Secondary: 55U35: Abstract and axiomatic homotopy theory

Keywords
symmetric spectrum

Citation

Schwede, Stefan. On the homotopy groups of symmetric spectra. Geom. Topol. 12 (2008), no. 3, 1313--1344. doi:10.2140/gt.2008.12.1313. https://projecteuclid.org/euclid.gt/1513800098

References

• M B ökstedt, Topological Hochschild homology, preprint, Bielefeld (1985)
• A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer, Berlin (1972)
• M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149–208
• M Lydakis, Smash products and $\Gamma$–spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999) 311–328
• M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. $(3)$ 82 (2001) 441–512
• G Segal, Categories and cohomology theories, Topology 13 (1974) 293–312
• B Shipley, Symmetric spectra and topological Hochschild homology, $K$–Theory 19 (2000) 155–183