Algebraic & Geometric Topology 7 (2007) 1963–1977

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 SP_h(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.

Keywords

homotopy colimit, infinite symmetric product, Barratt–Priddy–Quillen Theorem

Mathematical Subject Classification

Primary: 55Q10

Secondary: 55P42

References

Publication

Received: 10 April 2006
Accepted: 5 November 2007
Published: 18 December 2007

Authors