Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Bott-Chern and Aeppli cohomology   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.

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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph