Torsion in the homology of finite covers of 3-manifolds

TL;DR

This paper proves that for certain prime 3-manifolds, one can find finite covers with arbitrarily large torsion in their first homology group, extending understanding of homological torsion growth in 3-manifold covers.

Contribution

It demonstrates the existence of finite covers with arbitrarily large torsion in the first homology for a broad class of prime 3-manifolds, building on previous results.

Findings

Existence of finite covers with arbitrarily large torsion in H_1

Extension of torsion growth results to non-graph prime 3-manifolds

Use of prior theorems by Sun and Hadari to establish new bounds

Abstract

Let $N$ be a prime 3-manifold that is not a closed graph manifold. Building on a result of Hongbin Sun and using a result of Asaf Hadari we show that for every $k\in\Bbb{N}$ there exists a finite cover $\tilde{N}$ of $N$ such that $|\operatorname{Tor} H_1(\tilde{N};\Bbb{Z})|>k$.