ON THE COHOMOLOGY OF ALMOST-COMPLEX MANIFOLDS

Following [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom. 17(4) (2009) 651-683], 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 and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom. 17(4) (2009) 651-683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math. 36(1) (1976) 225-255] to study the cone of semi-Kahler structures on a compact semi-Kahler manifold.