Translation extensions of the classical modular group

Abstract

Abstract The class of Kleinian groups which are extreme with respect to Jorgensen's inequality encompasses continuous families of geometrically finite groups as well as uncountably many geometrically infinite groups, Such groups may be obtained as extensions of the classical modular group.An infinite number of non-isomorphic extreme discrete groups arise this way; some, like the Picard group, are of co-finite volume.Other examples are obtained by extending certain triangle groups. AMS No: 30F4020H10 *Alfred P. Sloan Research Fellow, partially supported by NSF-DMS-8807141. *Alfred P. Sloan Research Fellow, partially supported by NSF-DMS-8807141. Notes *Alfred P. Sloan Research Fellow, partially supported by NSF-DMS-8807141.