3 jul 2015 -- 14:00
Besides the Dolbeault cohomology, the Bott-Chern cohomology provides a further invariant in the geometry of complex non-Kähler manifolds. It also arises as a natural tool in investigating special Hermitian metrics. On the one side, the Bott-Chern cohomology may encode, in a sense, more informations on the complex and geometric structures. On the other side, it seems, algebraically, less "natural". As an example: the Frölicher inequality for the Dolbeault cohomology has an analogue for the Bott-Chern cohomology, which is stronger in the sense that the equality characterizes the validity of the ∂∂¯¯¯-Lemma. As a counter-example: it is not clear how far a theory of formality may be restated in terms of Bott-Chern cohomology: the talk would like to be an attempt to understand this issue.