²Strictly speaking this is only true on a spin manifold. Note that $\int \; <!--nolimits-->d^{4}x{\left(8\pi \right)}^{-1}{F}_{\mu \nu }{\tilde{F}}_{\mu \nu }=\pi \int \; <!--nolimits-->{\left(F∕2\pi \right)}^2=\pi \int \; <!--nolimits-->c_1{\left(F\right)}^2$. On a spin manifold, the intersection form is even, and the last expression is an integral multiple of $2\pi$. For the subtlety on non-spin manifolds, see [24].