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

DOI:
https://doi.org/10.1090/S0002-9939-05-08062-7

Published electronically:
August 29, 2005

MathSciNet review:
2196061

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the space of pointed continuous maps from a finite cell complex to a space . Let be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on and , will send an -isomorphism in either variable to a map that is monic in homology. Interesting examples arise by letting be -theory, the finite complex be a sphere, and the map in the 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

Email:
njk4x@virginia.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08062-7

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