The goal of this note is to outline the computation of the Adams spectral sequence of . Essentially all differentials follow from the Leibniz rule, and products can be computed with a computer. The only work to be done is to organize the computation in order to conclude that we have indeed computed all differentials.
To do so, we need a complete calculation of the Adams page, which was done by Davis and Mahowald  (in their notation, ). As usual, we have
This group is free over , where . Thus, to understand this group, it suffices to describe the generators under . In the Davis–Mahowald description, these generators fall into 4 groups, and we colour-coded these in our chart in Figure 1. We shall go through the different groups in the coming sections, giving a formal description and describe the differentials that pertain to these groups. The differentials up to degree are depicted in ??. The range – is fairly similar and is depicted in Figure 8. Finally, is permanent and so all differentials are -periodic.