On macroscopic dimension of rationally inessential manifolds

We show that, for a rationally inessential orientable closed n-manifold M whose fundamental group is a duality group, the macroscopic dimension of its universal cover (M)\tilde]\tilde M is strictly less than n: dim _MC (M)\tilde] < n\tilde M < n. As a corollary, we obtain the following partial result towards Gromov’s conjecture