GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911949548158976 |
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| author | Kuroki, Shintaro Uma, Vikraman |
| author_facet | Kuroki, Shintaro Uma, Vikraman |
| contents | We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions, i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_11598 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology Kuroki, Shintaro Uma, Vikraman Algebraic Topology Combinatorics We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions, i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$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. |
| title | GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology |
| topic | Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2106.11598 |