Divergence of projective structures and lengths of measured laminations

Details Divergence of projective structures and lengths of measured laminations Divergence of projective structures and lengths of measured laminations

1996-02-05

arxiv.org/abs/math/9602210v1

Mathematics

Complex Variables

Scientific paper

Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating that as the projective structures on a fixed complex structure diverge so do their monodromies. In course of arguments, we extend the concept of realization of laminations for PSL$(2,{\mathbf C})$-representations of surface groups.

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