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The spectrum (P ⋀ bo) −∞

Published online by Cambridge University Press:  24 October 2008

Donald M. Davis  and
Mark Mahowald
Donald M. Davis
Affiliation:
Lehigh University, Bethlehem, PA 18015
Mark Mahowald
Affiliation:
Northwestern University, Evanston, IL 60201
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Extract

There are spectra P−k constructed from stunted real projective spaces as in [1] such that H*(P−k) is the span in ℤ/2[x, x−1] of those xi with i ≥ −k. (All cohomology groups have ℤ/2-coefficients unless specified otherwise.) Using collapsing maps, these form an inverse system

which is similar to those of Lin ([15], p. 451). It is a corollary of Lin's work that there is an equivalence of spectra

where holim is the homotopy inverse limit ([3], ch. 5) and Ŝ–1 the 2-adic completion of a sphere spectrum. One may denote by this holim (P–κ), although one must constantly keep in mind that , but rather

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 85 - 93
Copyright
Copyright © Cambridge Philosophical Society 1984

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