Title: An Integral Version of the Brown-Gitler Spectrum
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 betw...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.Read More