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Complex projective structures on Kleinian groups

Albert Marden

Geometry & Topology Monographs 1 (1998) 335–340

DOI: 10.2140/gtm.1998.1.335

arXiv: math.GT/9810196

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 ∂M3≠∅. We will show that every homomorphism θ:π1(M3)→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 M3.

Keywords

projective structures on Riemann surfaces, hyperbolic 3–manifolds

Mathematical Subject Classification

Primary: 30F50

Secondary: 30C99, 30F45, 30F60, 30F99

References
Publication

Received: 1 June 1998
Published: 27 October 1998

Authors
Albert Marden
School of Mathematics
University of Minnesota
Minneapolis MN 55455
USA