Journal of Symplectic Geometry

Volume 12 (2014)

Number 2

Symplectic manifolds and cohomological decomposition

Pages: 215 – 236



Daniele Angella (Dipartimento di Matematica, Università di Pisa, Italy)

Adriano Tomassini (Dipartimento di Matematica e Informatica, Università di Parma, Italy)


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.

Published 13 May 2014