On a Spectrum-level Splitting of the $BP \langle 2 \rangle$-Cooperations Algebra

Abstract

In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo \wedge bo$ and $BP\langle 1 \rangle \wedge BP\langle 1 \rangle$. These splittings helped make it feasible to do computations using the $bo$- and $BP \langle 1 \rangle$-based Adams spectral sequences. In this paper, we construct an analogous splitting for $BP \langle 2 \rangle \wedge BP\langle 2 \rangle$.