An Interpolation between Homology and Stable Homotopy

Details An Interpolation between Homology and Stable Homotopy An Interpolation between Homology and Stable Homotopy

1998-10-12

arxiv.org/abs/math/9810068v1

Mathematics

Algebraic Topology

15 pages. Submitted for publication

Scientific paper

By considering labeled configurations of ``bounded multiplicity'', one can construct a functor that fits between homology and stable homotopy. Based on previous work, we are able to give an equivalent description of this labeled construction in terms of loop space functors and symmetric products. This yields a direct generalization of the May-Milgram model for iterated loop spaces, and answers questions of Carlsson and Milgram posed in the handbook. We give a classifying space formulation of our results hence extending an older result of Segal. We finally relate our labeled construction to a theory of Lesh and give a generalization of a well-known theorem of Quillen, Barratt and Priddy.

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