The Figure Eight Knot Group is Conjugacy Separable
S. C. Chagas, P. A. Zalesskii

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Finite Group Theory Research
