An integral version of the Brown-Gitler spectrum

Shimamoto, Don H.

doi:10.1090/S0002-9947-1984-0737876-X

An integral version of the Brown-Gitler spectrum
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Trans. Amer. Math. Soc. 283 (1984), 383-421 Request permission

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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