Low-degree mod-two cohomology of an Eilenberg–MacLane space (source code)

= Low-degree mod-two cohomology of an Eilenberg–MacLane space
{title2=$H^{\leq n+3}(K(\mathbb Z/2,n);\mathbb F_2)$}

For $n\geq2$, the positive-degree dimensions in degrees $n,n+1,n+2,n+3$ are $1,1,1,2$. The first three classes are $u,\operatorname{Sq}^1u,\operatorname{Sq}^2u$. In degree $n+3$, use $\operatorname{Sq}^3u$ and $\operatorname{Sq}^2\operatorname{Sq}^1u$ for $n\geq3$; at $n=2$ replace the unstable first class by $u\operatorname{Sq}^1u$. At $n=2$ the degree-four class is $u^2$, and at $n=3$ the degree-six class $\operatorname{Sq}^3u$ is $u^2$.