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An integral version of the Brown-Gitler spectrum


Author: Don H. Shimamoto
Journal: Trans. Amer. Math. Soc. 283 (1984), 383-421
MSC: Primary 55P42; Secondary 55P35, 55S10, 55S45, 57R19
DOI: https://doi.org/10.1090/S0002-9947-1984-0737876-X
MathSciNet review: 737876
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Abstract: In this paper, certain spectra $ {B_1}(k)$ are studied whose behavior qualifies them as being integral versions of the Brown-Gitler spectra $ B(k)$. The bulk of our work emphasizes the similarities between $ {B_1}(k)$ and $ B(k)$, shown mainly using the techniques of Brown and Gitler. In analyzing the homotopy type of $ {B_1}(k)$, we provide a free resolution over the Steenrod algebra for its cohomology and study its Adams spectral sequence. We also list conditions which characterize it at the prime $ 2$. The paper begins, however, on a somewhat different topic, namely, the construction of a configuration space model for $ {\Omega ^2}({S^3}\left\langle 3 \right\rangle )$ and other related spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0737876-X
Keywords: Brown-Gitler spectrum, Steenrod algebra, iterated loop space, Thom spectrum, $ \Lambda $-algebra, Adams spectral sequence, orientability of manifolds, Postnikov tower
Article copyright: © Copyright 1984 American Mathematical Society

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