GKM graph locally modeled by $T^n\times S^1$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology 

Shintaro Kuroki, Vikraman Uma

We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of 4n-dimensional manifolds with T n×S 1 -actions, i.e., GKM graphs of the toric hyperK¨ahler manifolds and of the cotangent bundles of toric manifolds. Under some conditions, the graph equivariant cohomology ring of such a labeled graph is computed. We also give a module basis of the graph equivariant cohomology by using a shelling structure of such a labeled graph, and study their multiplicative structure

Fields Institute Communications

Springer Nature Switzerland

179

238

https://doi.org/10.1007/978-3-031-57204-3_11