= Intersection form of a product of two closed oriented surfaces
{title2=$Q_{\Sigma_g\times\Sigma_h}\cong H^{\oplus(1+2gh)}$}
Here $H$ is the hyperbolic form with matrix $\begin{pmatrix}0&1\\1&0\end{pmatrix}$. The degree-two cohomology consists of the two factor orientation classes and $4gh$ products of degree-one classes. The factor classes pair once and have zero squares. In symplectic bases $a_i,b_i$ and $c_j,d_j$, $(a_ic_j)(b_kd_l)=-\delta_{ik}\delta_{jl}\omega_1\omega_2$ and $(a_id_j)(b_kc_l)=\delta_{ik}\delta_{jl}\omega_1\omega_2$. Each pair $(i,j)$ contributes two hyperbolic forms; the fiber classes contribute one more. The sign in the first formula comes from interchanging two odd-degree factors.
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