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2007 The homotopy infinite symmetric product represents stable homotopy
Christian Schlichtkrull
Algebr. Geom. Topol. 7(4): 1963-1977 (2007). DOI: 10.2140/agt.2007.7.1963

Abstract

We modify the definition of the infinite symmetric product of a based space X by applying the homotopy colimit instead of the colimit. This gives a topological monoid SPh(X) and using formal properties of homotopy colimits, we prove that its group completion represents the stable homotopy of X. In this way we get a streamlined approach to the Barratt–Priddy–Quillen theorem.

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Christian Schlichtkrull. "The homotopy infinite symmetric product represents stable homotopy." Algebr. Geom. Topol. 7 (4) 1963 - 1977, 2007. https://doi.org/10.2140/agt.2007.7.1963

Information

Received: 10 April 2006; Accepted: 5 November 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1131.55007
MathSciNet: MR2366183
Digital Object Identifier: 10.2140/agt.2007.7.1963

Subjects:
Primary: 55Q10
Secondary: 55P42

Keywords: Barratt–Priddy–Quillen Theorem , Homotopy colimit , infinite symmetric product

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 4 • 2007
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