Indecomposable Uniform Families on the Adams 4-Line

Abstract

We show that the $f_j$, $p_j$, $D_3(j)$, and $p_j'$ families on the 4-line of the classical Adams spectral sequence all conform to the Uniform Doomsday Conjecture. We do so by first using Bruner's formula to establish uniform families of differentials on these classes. We then study the Burklund-Xu and Cartan-Eilenberg spectral sequences to ensure that the differential targets are nonzero. The $f_j$ family requires further analysis of possible Adams $d_2$ differentials since the $f_j$ support uniform $d_3$ differentials. As a result of our work, only two indecomposable $\text{Sq}^0$ families remain to be settled in Adams filtration 4.