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
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.
Tags:
FIRB2012-DGGFT