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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The spectrum $ (P\wedge{\rm BP}\langle 2\rangle)\sb {-\infty}$


Authors: Donald M. Davis, David C. Johnson, John Klippenstein, Mark Mahowald and Steven Wegmann
Journal: Trans. Amer. Math. Soc. 296 (1986), 95-110
MSC: Primary 55P42; Secondary 55N22, 55T15
MathSciNet review: 837800
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Abstract: The spectrum $ {(P \wedge {\text{BP}}\langle {\text{2}}\rangle)_{ - \infty }}$ is defined to be the homotopy inverse limit of spectra $ {P_{ - k}} \wedge {\text{BP}}\langle {\text{2}}\rangle $, where $ {P_{ - k}}$ is closely related to stunted real projective spaces, and $ {\text{BP}}\langle {\text{2}}\rangle $ is formed from the Brown-Peterson spectrum. It is proved that this spectrum is equivalent to the infinite product of odd suspensions of the $ 2$-adic completion of the spectrum of connective $ K$-theory. An odd-primary analogue is also proved.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0837800-7
PII: S 0002-9947(1986)0837800-7
Keywords: Brown-Peterson spectrum, homotopy inverse limits, projective spaces, Adams spectral sequence
Article copyright: © Copyright 1986 American Mathematical Society