La science et l'hypothèse
《La science et l'hypothèse》 · 第 286–288 页 · Section 8.1，Definition 8.1.4 的四维流形条件、(b) 及临界点分析
Let \(X\) be a compact, connected, oriented, smooth 4-manifold. […] A Lefschetz fibration on \(X\) is a map \(\pi:X\to\Sigma\), where \(\Sigma\) is a compact, connected, oriented surface and \(\pi^{-1}(\partial\Sigma)=\partial X\), such that each critical point of \(\pi\) lies in \(\operatorname{int}X\) and has a local coordinate chart as in (a). […] Each critical point has a local coordinate chart in which \(\pi(z_1,z_2)=z_1z_2\). […] Equivalently, each critical point corresponds to an embedded surgery circle called a vanishing cycle in a nearby regular fiber, and the singular fiber is obtained by collapsing the vanishing cycle to a point to create a transverse self-intersection.