= Real de Rham intersection form in dimension four
{title2=$Q:H_{\mathrm{dR}}^2(N;\mathbb R)^2\to\mathbb R$}
On a compact oriented <smooth manifold> $N$ of dimension four without boundary, set $Q([\alpha],[\beta])=\int_N\alpha\wedge\beta$ for closed real two-forms. The <Stokes theorem> makes the expression independent of representatives, and the even degrees make it symmetric. It is the real <de Rham cohomology> version of the <intersection form>. The <Hodge decomposition theorem> and <Hodge star operator> express it as $Q(h,k)=(h,*k)_{L^2}$ on harmonic representatives.
Back to article page
