Prescribed virtual homological torsion of 3-manifolds

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 $M^{\prime }\to M$ so that $A$ is a direct factor in $H_1(M^{\prime },\mathbb{Z})$. This generalizes results of Sun and of Friedl-Herrmann.

13 pages, 1 figure

References in corpus (2)

• Systoles of hyperbolic 4-manifolds
• Torsion in the homology of finite covers of 3-manifolds