Journal of Symplectic Geometry

Volume 12 (2014)

Number 2

Symplectic manifolds and cohomological decomposition

Pages: 215 – 236

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n2.a1

Authors

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

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

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.

Full Text (PDF format)