On discrete generalised triangle groups

Abstract

A generalised triangle group has a presentation of the formwhere R is a cyclically reduced word involving both x and y. When R = xy, these classical triangle groups have representations as discrete groups of isometrics of S2, R2, H2 depending onIn this paper, for other words R, faithful discrete representations of these groups in Isom +H3 = PSL(2, C) are considered with particular emphasis on the case R = [x, y] and also on the relationship between the Euler characteristic χ and finite covolume representations.