Hereditary properties of co-Kähler manifolds

We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-Kähler manifolds. As a consequence, we prove that co-Kähler manifolds satisfy the Toral Rank Conjecture: dim(H⁎(M;Q))≥2r, for any r-torus Tr which acts almost freely on M.