Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The structure of certain subgroups of the Picard group

Norbert Wielenberga1

a1 Science Division, University of Wisconsin – Parkside, Kenosha, Wisconsin 53141, U.S.A.

A torsion-free discrete subgroup G of PSL(2, C) acts as a group of isometries of hyperbolic 3-space H3. The resulting quotient manifold M has H3 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 S3. 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.

(Received October 25 1977)


† Research supported in part by the National Science Foundation.