De Rham and Dolbeault cohomology of Cousin groups and Oeljeklaus-Toma manifolds
Alexandra-Iulia Otiman (Universita' Roma Tre)

Oeljeklaus-Toma (OT-) manifolds are a higher-dimensional generalization of Inoue-Bombieri surfaces and were introduced by K. Oeljeklaus and M. Toma in 2005. For any positive natural numbers s and t, OT manifolds of type (s,t) are quotients of $\mathbb{H}^s \times \mathbb{C}^t$ by discrete groups of affine transformations arising from a number field K and a particular choice of a subgroup of units U of K. In this talk, we compute their de Rham and Dolbeault cohomology by using the Leray-Serre spectral sequence and by relating their construction to certain domains contained in Cousin groups defined by lattices satisfying a strong dispersiveness condition. Moreover, we describe the cohomology groups in terms of some number-theoretical invariants and we prove that Hodge decomposition holds. In particular, we obtain a new way of computing the Dolbeault cohomology of Inoue-Bombieri surfaces. These results are part of a joint work with N. Istrati and a joint work with M. Toma.

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