Title: Primitive cohomology of real degree two on compact symplectic manifolds
Abstract: In this paper, we define the generalized Lejmi's P J operator on a compact almost Kähler 2n-manifold. We get that J is C ∞-pure and full if dim ker P J = b 2−1. Additionally, we investigate the relationship between J -anti-invariant cohomology introduced by T.-J. Li and W. Zhang and new symplectic cohomologies introduced by L.-S. Tseng and S.-T. Yau on a closed symplectic 4-manifold.