Epimorphisms between 2-bridge link groups

TL;DR

This paper systematically constructs epimorphisms between 2-bridge link groups and explores their topological and algebraic implications, including relations via singular maps and applications to character varieties and 3-manifold mappings.

Contribution

It introduces a method to construct and analyze epimorphisms between 2-bridge link groups, linking algebraic properties to topological maps with specific singularities.

Findings

Established a systematic construction of epimorphisms between 2-bridge link groups

Connected epimorphisms to maps with specific singularities between ambient spaces

Applied results to character varieties and pi_1-dominating maps in 3-manifolds

Abstract

We give a systematic construction of epimorphisms between 2-bridge link groups. Moreover, we show that 2-bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2-bridge links and pi_1-dominating maps among 3-manifolds.