Top-degree de Rham cohomology
= Top-degree de Rham cohomology
{title2=$H^n_{\mathrm{dR}}(M)$}
On a <compact> <connected> oriented $n$-dimensional <smooth manifold> without boundary, integration is a <linear isomorphism> $H^n_{\mathrm{dR}}(M)\to\mathbb R$. Thus two top-degree <differential forms> have the same <de Rham cohomology> class exactly when their integrals agree.