Geometry & Topology

On the homotopy groups of symmetric spectra

Stefan Schwede

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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


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