#### Jean F. Mattei

Université Paul Sabatier

### Resumen:

The goal is to describe the set on the topological classes of holomorphic foliations germs at the origin of C^2. We introduce notions of marking; We prove, under some assumptions, that when the Camacho-Sad indexes and the holonomy representations (which are topological invariants) are fixed, then the classes of marked foliations constitute an abelian group which is a finite extension of a quotient of C^N by a finitely generated subgroup. We compare this situation with the space of strongly marked foliation whose classification is given by the monodromy representation.

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