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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Formula for compositions of Steenrod squares that produce a form in the top degree
On a smooth $d$ dimensional compact connected manifold $M$, for an $\mathbb{Z}_2$-valued $(d-j)$-cocycle $x_{d-j}$ we have the formula ${\text{Sq}}^{j} (x_{d-j}) = u_{j} \cup x_{d-j}$. Here $u_j \in …