Topological Moduli Space for Germs of Holomorphic Foliations

Abstract

Abstract This work deals with the topological classification of germs of singular foliations on $(\mathbb{C}^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho–Sad indices, and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. This moduli space may be an infinite-dimensional functional space but under generic conditions we prove that it has finite dimension and we describe its algebraic and topological structure.