#### Volume 12, issue 3 (2008)

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On the homotopy groups of symmetric spectra

### Stefan Schwede

Geometry & Topology 12 (2008) 1313–1344
##### 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 ${\pi }_{\ast }$–isomorphisms, semistability and the relationship between naive and true homotopy groups for symmetric spectra.

##### Keywords
symmetric spectrum
Primary: 55P42
Secondary: 55U35