#### 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.

Notes on file formats
Albert Marden

School of Mathematics, University of Minnesota

Minneapolis, MN 55455, USA

Email: am@math.umn.edu

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