3 problems

Singer's conjecture. The homomorphism

Detection conjecture. The nonzero element $t$ is detected by the sixth algebraic transfer $Tr_6(\mathbb F_2)$.

Let $\mathscr A_2$ be the mod-$2$ Steenrod algebra, let $n_d$ be the internal degree sequence used in the paper, and let $Tr_5^{\mathscr A_2}$ denote the fifth algebraic transfer.…