Oeljeklaus-Toma manifolds are a higher dimension generalization of Inoue-Bombieri surfaces and were introduced by K. Oeljeklaus and M. Toma in 2005. They are quotients of H^s * C^t by discrete groups of affine transformations arising from a number field K and a particular choice of a subgroup of units U of K. They are commonly referred to as OT manifolds of type (s, t). OT manifolds have been of particular interest for locally conformally Kähler (lcK) geometry since they do not admit Kähler metrics, but those of type (s, 1) admit lcK metrics and for (s, t) in general, the existence of an lcK metric reduces to a numerical condition.
In this talk, we compute their de Rham and twisted cohomology and derive from this several characterization problems concerning their lcK geometry.