Decompositions Involving Anick’s Spaces

The goal of this work is to continue the investigation of the Anick fibration and the associated spaces. Recall that this is a p-local fibration sequence: ΩS πn −→ S −→ T −→ ΩS where πn is a compression of the p th power map on ΩS. This fibration was first described for p > 5 as the culmination of a 270 page book [A]. In [AG], the authors described an H space structure for the fibration sequence. Its relationship to EHP spectra was discussed [G3] as well as first steps to developing a universal property. Much work has been done since then to find a simpler construction, and this was obtained for p > 3 in [GT]. This new construction also reproduces the results of [AG]. It is in the context of these new methods that this work is developed and we assume a familiarity with [GT]. One of the main features of the construction is a certain fibration sequence: