Epimorphisms between 2-bridge link groups: Homotopically trivial simple loops on 2-bridge spheres

TL;DR

This paper characterizes null-homotopic simple loops on 2-bridge spheres and describes all epimorphisms between 2-bridge link groups that preserve upper meridian pairs.

Contribution

It provides a complete classification of null-homotopic loops and characterizes epimorphisms between 2-bridge link groups, advancing understanding of their algebraic and geometric structures.

Findings

Complete characterization of null-homotopic simple loops on 2-bridge spheres

Description of all upper-meridian-pair-preserving epimorphisms between 2-bridge link groups

Enhanced understanding of the relationship between link group epimorphisms and geometric loops

Abstract

We give a complete characterization of those essential simple loops on 2-bridge spheres of 2-bridge links which are null-homotopic in the link complements. By using this result, we describe all upper-meridian-pair-preserving epimorphisms between 2-bridge link groups.