Absolute profinite rigidity of some closed fibered hyperbolic 3-manifolds

TL;DR

This paper presents the first examples of closed fibered hyperbolic 3-manifolds with fundamental groups uniquely identified by their finite quotients, including the first non-orientable profinitely rigid hyperbolic 3-manifold.

Contribution

It provides the first known examples of such manifolds with fundamental groups distinguished by finite quotients, advancing understanding of profinite rigidity in 3-manifold groups.

Findings

First examples of closed fibered hyperbolic 3-manifolds with distinguished fundamental groups

First non-orientable profinitely rigid hyperbolic 3-manifold

Fundamental groups uniquely determined by their finite quotients

Abstract

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first example of a non-orientable profinitely rigid hyperbolic 3-manifold.