12 sep 2018 -- 14:30
We study results concerning the structure and the cohomological properties of locally conformally symplectic manifolds and solvmanifolds.
In non-K\"ahler geometry, the Hodge decomposition and the Hard Lefschetz Condition are very special properties that determine the cohomological aspects of the complex, respectively symplectic structure. We consider now the twisted case of such cohomological properties, namely, the case of locally conformally structures with Morse-Novikov cohomology and its almost-symplectic counterpart. In particular, examples are provided on Inoue surfaces and their generalization in higher dimension (the so-called Oeljeklaus-Toma manifolds), where algebraic number theory and geometry interact. More examples are given by structure results for locally conformally symplectic Lie algebras, that we classify in dimension 4.
The talk is based on joint works with Alexandra Otiman and Nicoletta Tardini, and Giovanni Bazzoni and Maurizio Parton, and Luis Ugarte.