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Mapping spaces and homology isomorphisms

Author: Nicholas J. Kuhn; \break with an appendix by Greg Arone; Nicholas J. Kuhn
Journal: Proc. Amer. Math. Soc. 134 (2006), 1237-1248
MSC (2000): Primary 55P35; Secondary 55N20, 55P42
Published electronically: August 29, 2005
MathSciNet review: 2196061
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Abstract: Let $\operatorname{Map}(K,X)$ 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 $X$, $\operatorname{Map}(K, X)$ 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, the finite complex $K$ be a sphere, and the map in the $X$ variable be an exotic unstable Adams map between Moore spaces.

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Additional Information

Nicholas J. Kuhn
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904

Received by editor(s): September 2, 2004
Received by editor(s) in revised form: November 8, 2004
Published electronically: August 29, 2005
Additional Notes: This research was partially supported by a grant from the National Science Foundation
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society

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