Torsion in the homology of finite covers of 3-manifolds

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 $k\in \mathbb{N}$ there exists a finite cover $\tilde{N}$ of $N$ such that $|\mathrm{Tor}{H}_1(\tilde{N};\mathbb{Z})|>k$.

9 pages