Grothendieck rigidity of 3-manifold groups

TL;DR

This paper proves that the fundamental groups of certain 3-manifolds with toroidal boundary are Grothendieck rigid, meaning their algebraic structure is uniquely determined by their profinite completions.

Contribution

It establishes the Grothendieck rigidity property for fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary, a significant advancement in 3-manifold group theory.

Findings

Fundamental groups of these 3-manifolds are Grothendieck rigid.

The result links topological properties with algebraic rigidity.

Provides new insights into the structure of 3-manifold groups.

Abstract

We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.