Complex hyperbolic free groups with many parabolic elements
نویسندگان
چکیده
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 〈a, b〉 in PU(2, 1) for which a, b, ab, ab, ab, ab and [a, b] all are mapped to parabolics.
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