On the cohomology of almost-complex manifolds

Following T.-J. Li, W. Zhang [Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li, W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.] and the results obtained by D. Sullivan in [Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.] to study the cone of semi-K\"ahler structures on a compact semi-K\"ahler manifold.