Hyperbolic 3-Manifolds Groups are Subgroup Conjugacy Separable

TL;DR

This paper proves that the fundamental groups of hyperbolic 3-manifolds are subgroup conjugacy separable, meaning non-conjugate finitely generated subgroups can be distinguished in finite quotients, advancing understanding of their algebraic structure.

Contribution

The paper establishes that all fundamental groups of hyperbolic 3-manifolds are subgroup conjugacy separable, a significant property in geometric group theory.

Findings

Fundamental groups of hyperbolic 3-manifolds are subgroup conjugacy separable.

Non-conjugate finitely generated subgroups can be distinguished in finite quotients.

Advances understanding of algebraic properties of hyperbolic 3-manifold groups.

Abstract

A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. It is proved that the fundamental group of a hyperbolic 3-manifold (closed or with cusps) is subgroup conjugacy separable.