On the Milnor number of non‐isolated singularities of holomorphic foliations and its topological invariance

Abstract

We define the Milnor number of a one-dimensional holomorphic foliation F as the intersection number of two holomorphic sections with respect to a compact connected component 𝐶 of its singular set. Under certain conditions, we prove that the Milnor number of F on a three-dimensional manifold with respect to 𝐶 is invariant by 𝐶 1 topological equivalences.