Geometria De Rham and Dolbeault cohomology of Cousin groups and Oeljeklaus-Toma manifolds Alexandra-Iulia Otiman
22-11-2018 - 14:30
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211
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 $mathbb{H}^s imes mathbb{C}^t$ 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.
org: VIVIANI Filippo
|
