The connective KO-theory of the Eilenberg-MacLane space K(Z_2,2), I: the E_2 page (2410.23094v1)

Abstract: We compute the $E_2$ page of the Adams spectral sequence converging to the connective KO-theory of the second mod 2 Eilenberg-MacLane space, $ko_(K(Z/2,2))$. This required a careful analysis of the structure of $H^(K(Z/2,2);Z_2)$ as a module over the subalgebra of the Steenrod algebra generated by $Sq^1$ and $Sq^2$. Complete analysis of the spectral sequence will be performed in a subsequent paper.