Complex hyperbolic free groups with many parabolic elements.

We consider in this work representations of the of the fundamental group of the 3-punctured sphere in PU(2,1) such that the boundary loops are mapped to PU(2,1) . We provide a system of coordinates on the corresponding representation variety, and analyse more specifically those representations corresponding to subgroups of (3,3,∞) -groups. In particular we prove that it is possible to construct representations of the free group of rank two $\la a,b\ra$ in PU(2,1) for which a , b , ab , ab −1 , ab 2 , a 2 b and [a,b] all are mapped to parabolics