= Intersection pairing on an oriented surface
{title2=$\omega:H_1(\Sigma_g;\mathbb Z)^2\to\mathbb Z$}
Represent one-dimensional <homology classes> on a closed oriented <topological surface> by transverse oriented curves and sum their signed crossing points. This gives a <bilinear form> that is skew-symmetric. A symplectic handle basis has matrix $\begin{pmatrix}0&I_g\\-I_g&0\end{pmatrix}$, which is unimodular. In particular, a class detected with intersection $1$ or $-1$ by another integral class is a <primitive homology class>: the detecting homomorphism splits its rank-one subgroup.
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