On the double suspension homomorphism at odd primes

Authors:
J. R. Harper and H. R. Miller

Journal:
Trans. Amer. Math. Soc. **273** (1982), 319-331

MSC:
Primary 55T15; Secondary 55P40, 55Q25, 55Q45, 55U99

DOI:
https://doi.org/10.1090/S0002-9947-1982-0664045-2

MathSciNet review:
664045

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Abstract: We work with the -term for spheres and the stable Moore space, given by the -algebra at odd primes. Writing and , we construct compatible maps and prove the Metastability Theorem: in homology induces an isomorphism for where stem degree, homological degree resulting from the bigrading of and . There is an operator corresponding to the Adams stable self-map of the Moore space and extends to . A corollary of the Metastability Theorem and the Localization Theorem of the second author is that the map induces an isomorphism on homology after inverting .

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0664045-2

Article copyright:
© Copyright 1982
American Mathematical Society