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Results tagged with steenrod-algebra
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user 9684
13
votes
Accepted
Derivations in the Steenrod algebra
The $D$ with $D(xy) = xD(y) + D(x)y$ are the primitives in the Steenrod algebra $A$, which are dual to the indecomposables $\xi_i$ in $A_* = F_2[\xi_i \mid i\ge1]$, so there is one such $D$ in each de …
- 9,263
16
votes
Accepted
Are all degree-1 cohomology operations Bocksteins?
Yes. For $i\ge1$ you can build $K(G,i)$ from the Moore space $M(G,i)$ by adding cells of dimension $\ge i+2$, so $H_i(K(G,i); Z) = G$ and $H_{i+1}(K(G,i); Z) = 0$. Hence $Ext(G, H) \cong H^{i+1}(K(G …
- 9,263
7
votes
specific modules over the Steenrod algebra with one generator
This realization problem is well-known in algebraic topology. Let $A$ denote the mod $2$ Steenrod algebra. For $k=0$ the module $A$ is the mod $2$ cohomology of $H\mathbb{Z}/2$, and for $k=1$ the mo …
- 9,263