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 $partialoverlinepartial$-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;
2014

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 `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 $partialoverlinepartial$-Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds.
Settore MAT/03 - Geometria
Mathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Complex Variables; Mathematics - Symplectic Geometry; 32Q99, 53D05, 53D18
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/58303
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