Virtual pro-$p$ properties of 3-manifold groups

TL;DR

This paper investigates the virtual pro-$p$ properties of 3-manifold groups, addressing a specific open question and exploring conjugacy $p$-separability in various classes of 3-manifolds.

Contribution

It provides new results on virtual $p$-efficiency and conjugacy $p$-separability for classes of 3-manifold groups, including Fuchsian groups and Seifert fiber spaces.

Findings

Resolved a question on virtual $p$-efficiency for 3-manifold groups.

Proved conjugacy $p$-separability for Fuchsian groups and Seifert fiber spaces.

Extended results to graph manifolds.

Abstract

We answer a question of Aschenbrenner and Friedl regarding virtual $p$-efficiency for 3-manifold groups. We then study conjugacy $p$-separability and prove results for Fuchsian groups, Seifert fibre spaces and graph manifolds.