  This work deals with the topological classification of singular foliation
germs 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 prove the existence of a
topological universal deformation through which every equisingular deformation
uniquely factorizes up to topological conjugacy. This is done by representing
the functor of topological classes of equisingular deformations of a fixed
foliation. We also describe the functorial dependence of this representation
with respect to the foliation.
