Symplectic manifolds, L^p-cohomology and q-parabolicity

Let $(M,\omega,J,g)$ be a non-compact almost K\"ahler manifold. In this paper we provide various criteria that assure that $\omega^k$ induces a non trivial class in the reduced $L^p$ maximal/minimal cohomology of $(M,g)$. Furthermore in the last part we explore some topological applications of our results.