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

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.

Theorems & Definitions (12)

• Lemma 2.1
• proof
• Theorem 2.2
• proof : Proof of Theorem \ref{['Mkthm']}
• Definition 3.3
• Proposition 3.5
• Proposition 3.7
• proof
• Theorem 3.9
• proof