Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds

Abstract

In this paper, we study the hard Lefschetz property of a symplectic manifold which admits a Hamiltonian torus action. More precisely, let $(M,\omega )$ be a 6-dimensional compact symplectic manifold with a Hamiltonian $T^2$-action. We will show that if the moment map image of $M$ is a GKM-graph and if the graph is index-increasing, then $(M,\omega )$ satisfies the hard Lefschetz property.

arXiv comment25 pages, final version (to appear in J. Symplectic Geom.)

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