ar X iv : m at h / 99 03 05 1 v 1 [ m at h . D G ] 9 M ar 1 99 9 ONE - SKELETONS AND EQUIVARIANT COHOMOLOGY

Motivated by the GKM picture of the equivariant cohomol-ogy ring for a torus action on an orbifold we define one-skeletons and their corresponding rings, H(Γ, α). We prove that, under a mild gener-icity condition, such a ring is a free S(g *)−module, with generators given by Thom classes of flow-outs of the vertices. We also show that many interesting notions and results in symplectic geometry, including symplectic reduction, blow-up, symplectic cutting and the ABBV local-ization theorem, have correspondents in the theory of one-skeletons.