Suspension Spectra and Homology Equivalences
- 1 May 1984
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 283 (1) , 303-313
- https://doi.org/10.2307/2000005
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.
Keywords
This publication has 16 references indexed in Scilit:
- Stable splittings derived from the Steinberg moduleTopology, 1983
- A Kahn-Priddy sequence and a conjecture of G. W. WhiteheadMathematical Proceedings of the Cambridge Philosophical Society, 1982
- The geometry of the James-Hopf mapsPacific Journal of Mathematics, 1982
- On Homology Equivalences and Homological Localizations of SpacesAmerican Journal of Mathematics, 1982
- Stable proofs of stable splittingsMathematical Proceedings of the Cambridge Philosophical Society, 1980
- The Boolean algebra of spectraCommentarii Mathematici Helvetici, 1979
- On the K -Theory of the Kahn-Priddy MapJournal of the London Mathematical Society, 1979
- Types of acyclicityJournal of Pure and Applied Algebra, 1974
- The nilpotency of elements of the stable homotopy groups of spheresJournal of the Mathematical Society of Japan, 1973
- Configuration-spaces and iterated loop-spacesInventiones Mathematicae, 1973