On the Bott-Chern and Aeppli cohomology

Abstract

This survey summarizes the results discussed in a talk at "Bielefeld Geometry & Topology Days" held at Bielefeld University in July 2015. We are interested in quantitative and qualitative properties of Bott-Chern cohomology. We announce new results obtained in [D. Angella, N. Tardini, Quantitative and qualitative cohomological properties for non-Kähler manifolds, arXiv:1507.07108] jointly with Nicoletta Tardini. In particular, we prove an upper bound of the dimensions of Bott-Chern cohomology in terms of Hodge numbers. We also introduce a notion, called Schweitzer qualitative property, which encodes the existence of a non-degenerate pairing in Bott-Chern cohomology, like the Poincaré duality for the de Rham cohomology. We show that this property characterizes the $\partial \overline{\partial }$-Lemma.

References in corpus (3)

• Autour de la cohomologie de Bott-Chern
• Koszulity of cohomology = $K(\pi ,1)$-ness + quasi-formality
• Volume and Self-Intersection of Differences of Two Nef Classes

Cited by in corpus (1)

• Extensions of $\overline{\partial }$-closed forms on compact generalized Hermitian manifolds