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

TL;DR

This paper explicitly defines Heckoid groups for 2-bridge links, and systematically constructs epimorphisms from 2-bridge link groups onto these groups, extending Riley's initial work.

Contribution

It provides a clear, systematic method for constructing epimorphisms from 2-bridge link groups onto Heckoid groups, generalizing Riley's original construction.

Findings

Explicit definition of Heckoid groups for 2-bridge links

Systematic construction method for epimorphisms

Generalization of Riley's initial construction

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.