The structure of certain subgroups of the Picard group

Abstract

A torsion-free discrete subgroup G of PSL (2, C ) acts as a group of isometries of hyperbolic 3-space H 3 . The resulting quotient manifold M has H 3 as its universal covering space with G as the group of cover transformations. We shall give examples where M has finite hyperbolic volume and is a link complement in S 3 . In these examples, G is a subgroup of the Picard group and in most cases is given as an HNN extension or a free product with amalgamation of kleinian groups with fuchsian groups as amalgamated or conjugated subgroups.