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EnglishWe 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 |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| 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 $\partial\overline\partial$-Lemma. As an application, we study cohomological properties of compact either complex, or symplectic, or, more in general, generalized-complex manifolds. |
| Handle: | http://hdl.handle.net/11384/58303 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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