Suspension spectra and homology equivalences

Kuhn, Nicholas J.

doi:10.1090/S0002-9947-1984-0735424-1

Suspension spectra and homology equivalences
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by Nicholas J. Kuhn PDF

Trans. Amer. Math. Soc. 283 (1984), 303-313 Request permission

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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