Computations regarding the torsion homology of Oeljeklaus-Toma manifolds

TL;DR

This paper explores the behavior of torsion homology in towers of Oeljeklaus-Toma manifolds, extending previous ideas from knot theory to higher homology groups and providing computational insights into their torsion growth.

Contribution

It extends the analysis of torsion homology growth from surfaces to higher-dimensional OT-manifolds and introduces computational methods for these cases.

Findings

Torsion in H_1 and H_2 grows exponentially in OT-manifolds of type S^0.

Torsion vanishes in all higher homology degrees.

Provides computational tools for studying higher-dimensional OT-manifolds.

Abstract

This article investigates the torsion homology behaviour in towers of Oeljeklaus-Toma (OT) manifolds. This adapts an idea of Silver and Williams from knot theory to OT-manifolds and extends it to higher degree homology groups. In the case of surfaces, i.e. Inoue surfaces of type $S^0$, the torsion grows exponentially in both $H_1$ (as was established by Braunling) and $H_2$ (our result) according to a parameter which already plays a role in Inoue's classical paper, and we obtain that the torsion vanishes in all higher degrees. This motivates our presented machine calculations for OT-manifolds of higher dimension.