Cohomological aspects on complex and symplectic manifolds
This is a survey paper that describes how Bott-Chern and Aeppli cohomology groups are important in the study of non-Kähler geometry. Namely, the topological invariants of the de Rham cohomology groups and the complex invariants of the Dolbeault cohomology groups are non-significant in the non-Kähler setting. The paper mainly describes previous results of the author and co-workers expecially related to the study of the \(\partial{\bar{\partial}}\)-lemma. Moreover, symplectic versions of the Bott-Chern and Aeppli cohomologies, introduced by \textit{L.-S. Tseng} and \textit{S.-T. Yau} [J. Differ. Geom. 91, No. 3, 383--416 (2012; Zbl 1275.53079)], are described and a characterization of the Hard Lefschetz Condition is given. For the entire collection see [Zbl 1387.53005].
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