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

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