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Abstract

Oeljeklaus–Toma (OT) manifolds are complex non-Kähler manifolds whose construction arises from specific number fields. 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 by averaging over a certain compact group, and the other one using the Leray–Serre spectral sequence. In addition, we compute also their twisted cohomology. As an application, we show that the low degree Chern classes of any complex vector bundle on an OT mani-
fold vanish in the real cohomology. Other applications concern the OT manifolds
admitting locally conformally Kähler (LCK) metrics: we show that there is only
one possible Lee class of an LCK metric, and we determine all the possible twisted
classes of an LCK metric, which implies the nondegeneracy of certain Lefschetz
maps in cohomology.