Complex projective structures on Kleinian groups

Albert Marden

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Complex projective structures on Kleinian groups

Albert Marden

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Abstract

Let M^3 be a compact, oriented, irreducible, and boundary incompressible 3-manifold. Assume that its fundamental group is without rank two abelian subgroups and its boundary is non-empty. We will show that every homomorphism from pi_1(M) to PSL(2,C) which is not `boundary elementary' is induced by a possibly branched complex projective structure on the boundary of a hyperbolic manifold homeomorphic to M.

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Albert Marden. 1998-10-27. Complex projective structures on Kleinian groups. https://arxiv.org/abs/math/9810196

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