Title: Cohomologies of locally conformally symplectic manifolds and solvmanifolds,
Abstract: 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 $S^0$.