In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of bo ∧ bo and l ∧ l. These splittings helped make it feasible to do computations using the bo- and l-based Adams spectral sequences. In this talk, we will sketch the construction of an analogous splitting for BP<2> ∧ BP<2> at primes larger than 3.
