Title: Mapping spaces and homology isomorphisms
Author: Nicholas J. Kuhn
AMS classification numbers: 55P35, 55N20, 55P42
arXiv no.: math.AT/0407146
address: University of Virginia, Charlottesville, VA USA
email: njk4x@virginia.edu

Abstract: 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 an 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.