Cohomological aspects in complex non-Kähler geometry
These notes give a comprehensive summary of results regarding various cohomology theories for compact complex manifolds which do not admit a Kähler structure, as well as some analogues in the case of almost complex manifolds. They are organized in four chapters. The first one recalls preliminary facts about complex and almost complex manifolds, Kähler manifolds, solvmanifolds, and deformations of complex structures. Chapter 2 deals with results regarding the Bott-Chern and Aeppli cohomologies, and their connection to the \(\partial\overline\partial\)-lemma, in the case of non-Kähler compact complex manifolds. Chapter 3 specializes to cohomological results for nilmanifolds, the Iwasawa manifold and its small deformations, and is a good source of examples of computations of the above mentioned cohomologies in these cases. Finally, Chapter 4 considers special subgroups of the de Rham cohomology of almost complex manifolds, related to the study of the tamed and the compatible symplectic cones. Throughout these notes, definitions and statements of the theorems are carefully presented, most proofs being omitted given the summary nature of the exposition. Nevertheless, the notes provide an excellent source of up-to-date results and references on the material presented.
scientific article; zbMATH DE number 6214473