On the Stiefel-Whitney classes of GKM manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909058533949440 |
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| author | Goertsches, Oliver Konstantis, Panagiotis Zoller, Leopold |
| author_facet | Goertsches, Oliver Konstantis, Panagiotis Zoller, Leopold |
| contents | We show that under standard assumptions on the isotropy groups of an integer GKM manifold, the equivariant Stiefel-Whitney classes of the action are determined by the GKM graph. This is achieved via a GKM-style description of the equivariant cohomology with coefficients in a finite field $\mathbb Z_{p}$ even though in this setting the restriction map to the fixed point set is not necessarily injective. This closes a gap in our argument why the GKM graph of a $6$-dimensional integer GKM manifold determines its nonequivariant diffeomorphism type. We introduce combinatorial Stiefel-Whitney classes of GKM graphs and use them to derive a nontrivial obstruction to realizability of GKM graphs in dimension $8$ and higher. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00528 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Stiefel-Whitney classes of GKM manifolds Goertsches, Oliver Konstantis, Panagiotis Zoller, Leopold Algebraic Topology 57R91, 55N91 We show that under standard assumptions on the isotropy groups of an integer GKM manifold, the equivariant Stiefel-Whitney classes of the action are determined by the GKM graph. This is achieved via a GKM-style description of the equivariant cohomology with coefficients in a finite field $\mathbb Z_{p}$ even though in this setting the restriction map to the fixed point set is not necessarily injective. This closes a gap in our argument why the GKM graph of a $6$-dimensional integer GKM manifold determines its nonequivariant diffeomorphism type. We introduce combinatorial Stiefel-Whitney classes of GKM graphs and use them to derive a nontrivial obstruction to realizability of GKM graphs in dimension $8$ and higher. |
| title | On the Stiefel-Whitney classes of GKM manifolds |
| topic | Algebraic Topology 57R91, 55N91 |
| url | https://arxiv.org/abs/2401.00528 |