Citation/Abstract

The homotopy groups of b o[Special characters omitted.] tmf are shown to be isomorphic to the homotopy groups of a wedge of suspensions of spectra related to integral Brown-Gitler spectra. We will then restate Mahowald's proof of the topological splitting of b o[Special characters omitted.] b o and subsequently apply similar techniques to construct a map that realizing the algebraic splitting of the homotopy of π _* ( b o[Special characters omitted.] tmf) as a topological splitting on the level of spectra. As an application, we use our results to provide ample groundwork demonstrating the splitting of the Tate spectrum of tmf.