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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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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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