Given a closed symplectic manifold, we study when the Lefschetz decomposition induced by the sl(2;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.
Symplectic manifolds and cohomological decomposition / Angella, Daniele; Tomassini, Adriano. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - STAMPA. - 12:(2014), pp. 215-236. [10.4310/JSG.2014.v12.n2.a1]
Symplectic manifolds and cohomological decomposition
ANGELLA, DANIELE;
2014
Abstract
Given a closed symplectic manifold, we study when the Lefschetz decomposition induced by the sl(2;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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