Mapping spaces and homology isomorphisms
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- by Nicholas J. Kuhn; \break with an appendix by Greg Arone; Nicholas J. Kuhn PDF
- Proc. Amer. Math. Soc. 134 (2006), 1237-1248 Request permission
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.References
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Additional Information
- Nicholas J. Kuhn
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- Email: njk4x@virginia.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1237-1248
- MSC (2000): Primary 55P35; Secondary 55N20, 55P42
- DOI: https://doi.org/10.1090/S0002-9939-05-08062-7
- MathSciNet review: 2196061