De Rham and twisted cohomology of Oeljeklaus-Toma manifolds

Nicolina Istrati, Alexandra Otiman

Published 2017-11-21Version 1

Oeljeklaus-Toma (OT) manifolds were introduced in \cite{ot} and their construction arises from specific number fields. They are complex non-K\"ahler manifolds, which represent higher dimension analogues of Inoue surfaces $\mathcal{S}^0$. In this note, we compute their de Rham cohomology in terms of invariants associated to the background number field. This is done by two distinct approaches, one using invariant cohomology and the other one using the Leray-Serre spectral sequence. Moreover, we compute also their twisted cohomology, which has a particular interest for the OT manifolds admitting a locally conformally K\"ahler metric. We focus on this last class of OT manifolds, which has proved to be a good ground for testing existing cohomological conjectures in locally conformally K\"ahler geometry. In particular, we show that there is only one possible Lee class for LCK metrics, namely the one occuring in \cite{ot}.