On the homotopy groups of symmetric spectra

Schwede, Stefan

doi:10.2140/gt.2008.12.1313

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On the homotopy groups of symmetric spectra

Stefan Schwede

Geometry & Topology 12 (2008) 1313–1344

DOI: 10.2140/gt.2008.12.1313

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.

Keywords

symmetric spectrum

Mathematical Subject Classification 2000

Primary: 55P42

Secondary: 55U35

References

Publication

Received: 30 September 2006

Accepted: 5 April 2008

Published: 3 June 2008

Proposed: Bill Dwyer

Seconded: Peter Teichner, Ralph Cohen

Authors

Stefan Schwede
Mathematisches Institut, Universität Bonn Beringstraße 3 53115 Bonn Germany

Volume 12, issue 3 (2008)