Closed and exact differential forms
= Closed and exact differential forms
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A <closed differential form> satisfies $d\alpha=0$; an <exact differential form> has $\alpha=d\beta$. The identity $d^2=0$ makes every exact form closed. Global failure of the converse is measured by <de Rham cohomology>; the <Poincaré lemma> gives the local converse in positive degrees.