  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.
