Journal of Symplectic Geometry

Volume 16 (2018)

Number 6

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

Pages: 1549 – 1590



Yunhyung Cho (Department of Mathematics Education, Sungkyunkwan University, Seoul, South Korea)

Min Kyu Kim (Department of Mathematics Education, Gyeongin National University of Education, Incheon, South Korea)


Let $(M, \omega)$ be a $6$-dimensional closed symplectic manifold with a Hamiltonian $T^2$-action. We show that if the action is GKM and its GKM graph is index-increasing, then $(M, \omega)$ satisfies the hard Lefschetz property.

Received 8 July 2014

Accepted 23 February 2018

Published 18 March 2019