TY - JOUR T1 - Doulbeault and J-invariant Cohomologies on Almost Complex Manifolds JF - Complex Analysis and Operator Theory Y1 - 2021 A1 - Lorenzo Sillari A1 - Adriano Tomassini KW - Almost Complex Manifolds KW - Cohomology of Lie Algebra KW - Compact four-manifold KW - Dolbeault Cohomology KW - Frölicher Spectral Sequence KW - Solvmanifold AB - In this paper we relate the cohomology of $J$-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given. VL - 15 UR - https://link.springer.com/article/10.1007/s11785-021-01156-w ER -