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 $S^0$.

References in corpus (3)

• Locally conformal Hermitian metrics on complex non-Kähler manifolds
• Quantitative and qualitative cohomological properties for non-Kähler manifolds
• Hodge theory for twisted differentials

Cited by in corpus (3)

• Symplectic cohomologies and deformations
• On certain class of locally conformal symplectic structures of the second kind
• The hard Lefschetz duality for locally conformally almost Kähler manifolds