Homological approximations for Profinite and Pro-$p$ limit groups

TL;DR

This paper investigates homological properties of the profinite completion of limit groups, extending known theorems to the profinite setting and providing new insights into their algebraic structure.

Contribution

It introduces homological approximation techniques for profinite completions of limit groups and proves an analogue of Bridson and Howie's theorem in this context.

Findings

Homological approximations of profinite completions are established.

An analogue of Bridson and Howie's theorem for non-abelian limit groups is proved.

The results deepen understanding of the algebraic and homological structure of limit groups.

Abstract

We study homological approximations of the profinite completion of a limit group (see Thm.~A) and obtain the analogous of Bridson and Howie's Theorem for the profinite completion of a non-abelian limit group (see Thm.~B).