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

Yunhyung Cho; Min Kyu Kim

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

Symplectic Geometry 2018-12-27 v2

Authors: Yunhyung Cho , Min Kyu Kim

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.

Keywords

hard lefschetz property hamiltonian torus action gkm manifolds symplectic manifold moment map gkm graph

Cite

@article{arxiv.1310.8405,
  title  = {Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds},
  author = {Yunhyung Cho and Min Kyu Kim},
  journal= {arXiv preprint arXiv:1310.8405},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

Cite

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