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.

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