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Suspension spectra and homology equivalences


Author: Nicholas J. Kuhn
Journal: Trans. Amer. Math. Soc. 283 (1984), 303-313
MSC: Primary 55P42; Secondary 55N20, 55P47, 55P60
DOI: https://doi.org/10.1090/S0002-9947-1984-0735424-1
MathSciNet review: 735424
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Abstract: Let $ f:{\Sigma ^\infty }X \to {\Sigma ^\infty }Y$ be a stable map between two connected spaces, and let $ {E_{\ast}}$ be a generalized homology theory. We show that if $ {E_{\ast}}(f)$ is an isomorphism then $ {E_{\ast}}({\Omega ^\infty }f):{E_{\ast}}(QX) \to {E_{\ast}}(QY)$ is a monomorphism, but possibly not an epimorphism. Applications of this theorem include results of Miller and Snaith concerning the $ K$-theory of the Kahn-Priddy map.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0735424-1
Article copyright: © Copyright 1984 American Mathematical Society

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