Cohomologies of locally conformally symplectic manifolds and solvmanifolds

We study the Morse–Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz condition. We consider solvmanifolds and Oeljeklaus–Toma manifolds. In particular, we prove that Oeljeklaus–Toma manifolds with precisely one complex place, and under an additional arithmetic condition, satisfy the Mostow property. This holds in particular for the Inoue surface of type S0S0.