Symplectic manifolds and cohomological decomposition

Abstract

Given a closed symplectic manifold, we study when the Lefschetz decomposition induced by the $\mathfrak{sl}(2;\mathbb{R})$-representation yields a decomposition of the de Rham cohomology. In particular, this holds always true for the second de Rham cohomology group, or if the symplectic manifold satisfies the Hard Lefschetz Condition.

Cited by in corpus (3)

• $L^2$-hard Lefschetz complete symplectic manifolds
• Symplectic cohomologies and deformations
• On cohomological decomposition of generalized-complex structures