Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincaré domain

Abstract

We show that the topological equivalence class of holomorphic foliation germs of rank 1 with an isolated singularity of Poincaré type is determined by the topological equivalence class of the real intersection foliation of the (suitably normalized) foliation germ with a sphere centered in the singularity. We use this Reconstruction Theorem to completely classify topological equivalence classes of plane holomorphic foliation germs of Poincaré type and discuss a conjecture on the classification in dimension ≥3.