Geometria Complessa e Geometria Differenziale
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D. Angella

On the Bott-Chern and Aeppli cohomology

created by daniele on 08 Nov 2016
modified on 17 Nov 2017


Inserted: 8 nov 2016
Last Updated: 17 nov 2017

Journal: Bielefeld Geometry & Topology Days
Year: 2016

ArXiv: 1507.07112 PDF

Published Online

Links: Bielefeld Geometry & Topology Days, arXiv:1507.07112


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-K\"ahler 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 Poincar\'e duality for the de Rham cohomology. We show that this property characterizes the $\partial\overline\partial$-Lemma.

Tags: FIRB2012-DGGFT

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