Intersection pairing
= Intersection pairing
{title2=$H_k(W)\times H_{n-k}(W,\partial W)\to F$}
An intersection pairing counts signed intersections of transverse representatives of complementary <homology classes>, using one relative representative when the <manifold> has boundary. With $\mathbb F_2$ coefficients it is defined without <orientation> choices. <Poincare-Lefschetz duality> makes this a <perfect pairing> for compact <manifolds>.