Quantitative and qualitative cohomological properties for non-Kähler manifolds

Abstract

We introduce a "qualitative property" for Bott-Chern cohomology of complex non-Kähler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the validity of the $\partial \overline{\partial }$-Lemma. This follows from a quantitative study of Bott-Chern cohomology. In this context, we also prove a new bound on the dimension of the Bott-Chern cohomology in terms of the Hodge numbers. We also give a generalization of this upper bound, with applications to symplectic cohomologies.

Cited by in corpus (8)

• On local stabilities of $p$-Kähler structures
• On the deformed Bott-Chern cohomology
• On the cohomology of almost complex and symplectic manifolds and proper surjective maps
• Cohomologies of locally conformally symplectic manifolds and solvmanifolds
• On non-Kähler degrees of complex manifolds
• Geometric formalities along the Chern-Ricci flow
• Balanced and Aeppli Parameters for the Heterotic Moduli
• The $\partial \bar{\partial }$-lemma under surjective maps