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 à la Frölicher 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 à la Frölicher characterizes the validity of the so-called cohomological property of satisfying the $partialoverlinepartial$-Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds.
Inequalities à la Frölicher and cohomological decompositions / Angella, Daniele; Tomassini, Adriano. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - STAMPA. - 9:(2015), pp. 505-542. [10.4171/JNCG/199]
Inequalities à la Frölicher and cohomological decompositions
ANGELLA, DANIELE;Tomassini, Adriano
2015
Abstract
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 à la Frölicher 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 à la Frölicher characterizes the validity of the so-called cohomological property of satisfying the $partialoverlinepartial$-Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds.File | Dimensione | Formato | |
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