Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Angella - A. Tomassini

Inequalities à la Frölicher and cohomological decompositions

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


Published Paper

Inserted: 8 nov 2016
Last Updated: 17 nov 2017

Journal: J. Noncommut. Geom.
Volume: 9
Number: 2
Pages: 505-542
Year: 2015
Doi: 10.4171/JNCG/199

ArXiv: 1403.2298 PDF


We study Bott-Chern and Aeppli cohomologies of a vector space endowed with two anti-commuting endomorphisms whose square is zero. In particular, we prove an inequality \`a la Fr\"olicher relating the dimensions of the Bott-Chern and Aeppli cohomologies to the dimensions of the Dolbeault cohomologies. We prove that the equality in such an inequality \`a la Fr\"olicher characterizes the validity of the so-called cohomological property of satisfying the $\partial\overline{\partial}$-Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds.

Tags: FIRB2012-DGGFT

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