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 ∂∂-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.
Quantitative and qualitative cohomological properties for non-KÄhler manifolds / Angella, D.; Tardini, N.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 145:1(2017), pp. 273-285. [10.1090/proc/13209]
|Appare nelle tipologie:||1.1 Articolo su rivista|