  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.
