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

TL;DR

This paper characterizes all upper-meridian-pair-preserving epimorphisms from 2-bridge link groups onto even Heckoid groups, confirming they are precisely those constructed systematically in prior work.

Contribution

It provides a complete characterization of specific epimorphisms from 2-bridge link groups onto even Heckoid groups, confirming their systematic construction as the only such epimorphisms.

Findings

All such epimorphisms are exactly those obtained by the systematic construction.

The characterization is complete for upper-meridian-pair-preserving epimorphisms.

The results extend the understanding of the relationship between 2-bridge link groups and Heckoid groups.

Abstract

In Part I of this series of papers, we made Riley's definition of Heckoid groups for 2-bridge links explicit, and gave a systematic construction of epimorphisms from 2-bridge link groups onto Heckoid groups, generalizing Riley's construction. In this paper, we give a complete characterization of upper-meridian-pair-preserving epimorphisms from 2-bridge link groups onto even Heckoid groups, by proving that they are exactly the epimorphisms obtained by the systematic construction.