On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds

Abstract

We answer a question of Oprea–Tralle on the realizability of symplectic algebras by symplectic manifolds in dimensions divisible by four, along with a question of Lupton–Oprea in all even dimensions. This will also allow us to address, in all even dimensions six and higher, another question of Oprea–Tralle on the possibility of algebraic conditions on the rational homotopy minimal model of a closed smooth manifold implying the existence of a symplectic structure on the manifold.