Suspension spectra and homology equivalences
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- by Nicholas J. Kuhn
- Trans. Amer. Math. Soc. 283 (1984), 303-313
- DOI: https://doi.org/10.1090/S0002-9947-1984-0735424-1
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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.References
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Bibliographic Information
- © Copyright 1984 American Mathematical Society
- 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