Euler number equals self-intersection
= Euler number equals self-intersection
{c}
{title2=$\langle e(\nu_S),[S]\rangle=[S]\cdot[S]$}
For an oriented closed surface smoothly embedded in an oriented four-manifold, a transverse section of the <normal bundle> gives a homologous small push-off. Its signed zeros are exactly the signed intersections with the original surface. This identifies the evaluation of the <Euler class> with the <self-intersection number>.