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

doi:10.1007/978-3-031-57204-3_11

paper

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

arXiv:2106.11598 · doi:10.1007/978-3-031-57204-3_11

Abstract

We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of $4 n$ -dimensional manifolds with $T^{n} \times S^{1}$ -actions, i.e., GKM graphs of the toric hyperK $a ¨$ hler 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.

52 pages, 16 figures; v2: correct some parts and add some figures

GKM graph locally modeled by Tn×S1-action on T∗Cn and its graph equivariant cohomology

Abstract

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