Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 16, pages 335-340.

Complex projective structures on Kleinian groups

Albert Marden

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.

Keywords. Projective structures on Riemann surfaces, hyperbolic 3-manifolds

AMS subject classification. Primary: 30F50. Secondary: 30F45, 30F60, 30F99, 30C99.

E-print: arXiv:math.GT/9810196

Submitted: 1 June 1998. Published: 27 October 1998.

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Albert Marden
School of Mathematics, University of Minnesota
Minneapolis, MN 55455, USA
Email: am@math.umn.edu

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