Mapping spaces and homology isomorphisms

Details Mapping spaces and homology isomorphisms Mapping spaces and homology isomorphisms

2004-07-08

arxiv.org/abs/math/0407146v1

Mathematics

Algebraic Topology

13 pages

Scientific paper

Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E_* be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on K and X, Map(K, X) will send a E_*--isomorphism in either variable to a map that is monic in E_* homology. Interesting examples arise by letting E_* be K--theory, K be a sphere, and the map in the X variable be an exotic unstable Adams map between Moore spaces.

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