For GKM3 actions, restriction maps in equivariant graph cohomology are surjective on abstract graph extensions, giving generator-relation descriptions of cohomology rings for Hamiltonian GKM4 actions.
Franz,A quotient criterion for syzygies in equivariant cohomology, Transformation Groups22(2016), 933–965
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Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM$_4$ manifolds
For GKM3 actions, restriction maps in equivariant graph cohomology are surjective on abstract graph extensions, giving generator-relation descriptions of cohomology rings for Hamiltonian GKM4 actions.