Studies of the torsion in the homology of Oeljeklaus–Toma manifolds

This article investigates the torsion homology behaviour in towers of Oeljeklaus–Toma (OT) manifolds. This adapts an idea of Silver–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 Bräunling) 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 one dimension higher.