The Omega spectrum for Pengelley's BoP

Abstract

We compute the homology of the spaces in the Omega spectrum for $BoP$. There is no torsion in $H_*(\underline{BoP}_{\; i})$ for $i \ge 2$, and things are only slightly more complicated for $i < 2$. We find the complete homotopy type of $\underline{BoP}_{\; i}$ for $i \le 6$ and conjecture the homotopy type for $i > 6$. This completes the computation of all $H_*(\underline{MSU}_{\;*})$.