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Transactions of the American Mathematical Society
Journal Article

Suspension Spectra and Homology Equivalences

Nicholas J. Kuhn
Transactions of the American Mathematical Society
Vol. 283, No. 1 (May, 1984), pp. 303-313
Published by: American Mathematical Society
DOI: 10.2307/2000005
https://www.jstor.org/stable/2000005
Page Count: 11

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Topics: Mathematical theorems, Functors, Commutativity, Connected regions, Adjoints, Geometric topology
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Suspension Spectra and Homology Equivalences
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Abstract

Let f: Σ∞ X → Σ∞ Y be a stable map between two connected spaces, and let E* be a generalized homology theory. We show that if E*(f) is an isomorphism then E*(Ω∞ f): E*(QX) → E*(QY) is a monomorphism. But possibly not an not an epimorphism. Applications of this theorem include results of Miller and Snaith concerning the K-theory of the Kahn-Priddy map.
Transactions of the American Mathematical Society © 1984 American Mathematical Society