Complex projective structures on Kleinian groups
Abstract
Let M3 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 pi1(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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