2024/06/21 by Phan, Dung Phuong, Bui, Tuan Anh, Rahm, Alexander D.
#Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2406.14942
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 S0, the torsion grows exponentially in both H1 (as was established by Braunling) and H2 (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.