## Journal of Symplectic Geometry

### Symplectical 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.

#### Article information

Source
J. Symplectic Geom., Volume 12, Number 2 (2014), 215-236.

Dates
First available in Project Euclid: 29 August 2014