# Cohomologies of locally conformally symplectic manifolds and solvmanifolds

created by daniele on 17 Mar 2017
modified on 18 Jan 2018

[BibTeX]

Published Paper

Inserted: 17 mar 2017
Last Updated: 18 jan 2018

Journal: Ann. Global Anal. Geom.
Volume: 53
Number: 1
Pages: 67--96
Year: 2018
Doi: 10.1007/s10455-017-9568-y

ArXiv: 1703.05512 PDF
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 $S^0$.