On the homotopy groups of symmetric spectra

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. © 2008 Geometry & Topology.