Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain (Q2421919)

The authors prove a Reconstruction Theorem for singular holomoprhic foliations germs on \((\mathbb{C}^2, 0)\). This means that the topological equivalence class of holomorphic foliation germs 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 3-dimensional sphere centered at the singularity \(0\). As an application of the Reconstruction Theorem, a complete topological classification of plane holomorphic foliation germs of Poincaré type is provided. A conjecture on the analogous classification on \((\mathbb{C}^3, 0)\) is discused The present results are related to [\textit{D. Marín} et al., Ann. Sci. Éc. Norm. Supér. (4) 45, No. 3, 405--445 (2012; Zbl 1308.32036)] on \((\mathbb{C}^2, 0)\), and [\textit{B. Limón} et al., J. Topol. 4, No. 3, 667--686 (2011; Zbl 1238.32024)] in the Morse and \(n\)-dimensional case.