Prescribed virtual homological torsion of 3-manifolds

TL;DR

This paper demonstrates that for any finite abelian group and certain 3-manifolds, there exists a finite cover where the group appears as a direct factor in the first homology, extending previous results.

Contribution

It generalizes prior work by showing the prescribed homological torsion can be realized in covers of non-graph 3-manifolds with boundary.

Findings

Existence of finite covers with prescribed abelian torsion

Extension of Sun and Friedl-Herrmann's results

Applicable to irreducible 3-manifolds with boundary

Abstract

We prove that given any finite abelian group $A$ and any irreducible $3$-manifold $M$ with empty or toroidal boundary which is not a graph manifold there exists a finite cover $M' \to M$ so that $A$ is a direct factor in $H_1(M',\mathbb{Z})$. This generalizes results of Sun and of Friedl-Herrmann.