De Rham–Weil theorem

In algebraic topology, the De Rham-Weil theorem allows computation of sheaf cohomology using an acyclic resolution of the sheaf in question.

Let $\mathcal F$ be a sheaf on a topological space $X$ and $\mathcal F^\bullet$ a resolution of $\mathcal F$ by acyclic sheaves. Then

$H^q(X,\mathcal F) \cong H^q(\mathcal F^\bullet(X)),$

where $H^q(X,\mathcal F)$ denotes the $q$-th sheaf cohomology group of $X$ with coefficients in $\mathcal F.$

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This article incorporates material from De Rham-Weil theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.