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.
|Titolo:||Inequalities à la Frölicher and cohomological decompositions|
|Data di pubblicazione:||2014|
|Parole Chiave:||Mathematics - Differential Geometry; Mathematics - Differential Geometry; Mathematics - Complex Variables; Mathematics - Symplectic Geometry; 32Q99, 53D05, 53D18|
|Appare nelle tipologie:||1.1 Articolo in rivista|