On the homotopy groups of symmetric spectra

Schwede, Stefan¹

¹ Mathematisches Institut, Universität Bonn, Beringstraße 3, 53115 Bonn, Germany

Geometry & topology, Tome 12 (2008) no. 3, pp. 1313-1344.

Résumé

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 ${\pi }_{\ast }$–isomorphisms, semistability and the relationship between naive and true homotopy groups for symmetric spectra.

Détail

DOI : 10.2140/gt.2008.12.1313

Keywords: symmetric spectrum

Bibliographie

[1] M Bökstedt, Topological Hochschild homology, preprint, Bielefeld (1985)

[2] A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972)

[3] M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149

[4] M Lydakis, Smash products and $\Gamma$–spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999) 311

[5] M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. $(3)$ 82 (2001) 441

[6] G Segal, Categories and cohomology theories, Topology 13 (1974) 293

[7] B Shipley, Symmetric spectra and topological Hochschild homology, $K$–Theory 19 (2000) 155