Resumen de Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

Andrea Cattaneo, Nicoletta Tardini, Adriano Tomassini

• Let (X,J,g,ω) be a compact 2n dimensional almost-Kähler manifold. We prove primitive decompositions of ∂, ¯∂¯-harmonic forms on X in bidegree (1,1) and (n−1,n−1) (such bidegrees appear to be optimal). We provide examples showing that in bidegree (1,1) the ∂- and ¯∂¯-decompositions differ.