The Hopf ring for bobo and its connective covers

In this work we recompute the known ordinary mod2 homology of the spectrum bobo as a Hopf ring. In addition, our study computes the Hopf modules over the Hopf ring H∗bo¯∗ for the connective covers bo〈1〉,bo〈2〉bo〈1〉,bo〈2〉, and bo〈4〉bo〈4〉. These results are calculated using the bar spectral sequence, which allows us to advance from one space to the next in the spectrum, and by using maps from our spectra to the mod2 Eilenberg–Mac Lane spectrum H¯ in order to facilitate the simplification of our result. These calculations yield, in turn, the Hopf ring for bo〈n〉bo〈n〉 for all nn.