Epimorphisms from 2-bridge link groups onto Heckoid groups (I)

Abstract

Riley "defined'' the Heckoid groups for $2$-bridge links as Kleinian groups, with nontrivial torsion, generated by two parabolic transformations, and he constructed an infinite family of epimorphisms from $2$-bridge link groups onto Heckoid groups. In this paper, we make Riley's definition explicit, and give a systematic construction of epimorphisms from $2$-bridge link groups onto Heckoid groups, generalizing Riley's construction.