Geometry & Topology

On the homotopy groups of symmetric spectra

Stefan Schwede

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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

Geom. Topol., Volume 12, Number 3 (2008), 1313-1344.

Received: 30 September 2006
Accepted: 5 April 2008
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P42: Stable homotopy theory, spectra
Secondary: 55U35: Abstract and axiomatic homotopy theory

symmetric spectrum


Schwede, Stefan. On the homotopy groups of symmetric spectra. Geom. Topol. 12 (2008), no. 3, 1313--1344. doi:10.2140/gt.2008.12.1313.

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