Computations regarding the torsion homology of Oeljeklaus-Toma 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 $H_1$ and $H_2$ according to a parameters which already plays a role in Inoue's classical paper. This motivates running example calculations in all homological degrees.