Poisson--Furstenberg boundaries of fundamental groups of closed 3-manifolds

TL;DR

This paper characterizes the Poisson--Furstenberg boundaries for fundamental groups of all closed 3-manifolds, extending previous results and providing a comprehensive understanding of these boundaries in geometric group theory.

Contribution

It provides a unified description of Poisson--Furstenberg boundaries for fundamental groups of all closed 3-manifolds, building on prior work for specific classes.

Findings

Descriptions of Poisson--Furstenberg boundaries for fundamental groups of compact graph-manifolds

Extension of boundary descriptions to all closed 3-manifolds

Integration with previous results by Kaimanovich and others

Abstract

We obtain a description of Poisson--Furstenberg boundaries for (random walks on) fundamental groups of compact graph-manifolds. Together with previously known results due to V.A. Kaimanovich and others, this allows one to obtain descriptions of Poisson--Furstenberg boundaries for fundamental groups of all closed 3-manifolds.