Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Workshop "Bielefeld Geometry & Topology Days"

On the Bott-Chern and Aeppli cohomology

Daniele Angella (Dipartimento di Matematica e Informatica "Ulisse Dini", Università di Firenze)

created by daniele on 13 Apr 2015
modified on 20 May 2015

3 jul 2015 -- 14:00

Bielefeld University


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.

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