Geodesic
The homotopy infinite symmetric product represents stable homotopy
Schlichtkrull, Christian1
1Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1963-1977
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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.

DOI : 10.2140/agt.2007.7.1963
Keywords: homotopy colimit, infinite symmetric product, Barratt–Priddy–Quillen Theorem

Schlichtkrull, Christian  1

1 Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway 
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Schlichtkrull, Christian. The homotopy infinite symmetric product represents stable homotopy. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 1963-1977. doi: 10.2140/agt.2007.7.1963

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