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In this paper we study the topological moduli space of some germs of singular holomorphic foliations in (C 2 , 0). We obtain a fully characterization for generic foliations whose vanishing order at the origin is two or three. We give a similar description for a certain subspace in the moduli space of generic germs of homogeneous foliations of any vanishing order and also for generic quasi-homogeneous foliations. In all the cases we identify the fundamental group of these spaces using thedoi:10.1007/s00014-003-0771-z fatcat:btwwtrzjdfgrhch6gkspoem634