Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM$_4$ manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914475257364480 |
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| author | Goertsches, Oliver Solomadin, Grigory |
| author_facet | Goertsches, Oliver Solomadin, Grigory |
| contents | Given a GKM$_3$ action of a torus $K$ on a manifold $M$ with GKM graph $Γ$, we show that for any extension of $Γ$ to an abstract GKM graph the corresponding restriction map in equivariant graph cohomology is surjective. While the corresponding statement for extensions of actions is well-known, we observe that this graph-theoretical statement is false in the GKM$_2$ setting. As a corollary, we obtain a description of the equivariant cohomology ring of Hamiltonian and complexity one GKM$_4$ actions in terms of generators and relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM$_4$ manifolds Goertsches, Oliver Solomadin, Grigory Algebraic Topology Given a GKM$_3$ action of a torus $K$ on a manifold $M$ with GKM graph $Γ$, we show that for any extension of $Γ$ to an abstract GKM graph the corresponding restriction map in equivariant graph cohomology is surjective. While the corresponding statement for extensions of actions is well-known, we observe that this graph-theoretical statement is false in the GKM$_2$ setting. As a corollary, we obtain a description of the equivariant cohomology ring of Hamiltonian and complexity one GKM$_4$ actions in terms of generators and relations. |
| title | Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM$_4$ manifolds |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2604.13629 |