The Figure Eight Knot Group is Conjugacy Separable

TL;DR

This paper proves that certain torsion-free subgroups related to Euclidean Bianchi groups are conjugacy separable, establishing a significant property in geometric group theory and hyperbolic geometry.

Contribution

It demonstrates conjugacy separability for torsion-free subgroups of PGL(2,C) commensurable with Euclidean Bianchi groups, a novel result in the field.

Findings

Torsion-free subgroups of PGL(2,C) are conjugacy separable.

Conjugacy separability applies to groups commensurable with Euclidean Bianchi groups.

The result confirms a conjecture related to the Figure Eight knot group.

Abstract

We prove that torsion free subgroups of PGL(2,C) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the title.