Reconstructing the orbit type stratification of a torus action from its equivariant cohomology
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916176794222592 |
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| author | Goertsches, Oliver Zoller, Leopold |
| author_facet | Goertsches, Oliver Zoller, Leopold |
| contents | We investigate what information on the orbit type stratification of a torus action on a compact space is contained in its rational equivariant cohomology algebra. Regarding the (labelled) poset structure of the stratification we show that equivariant cohomology encodes the subposet of ramified elements. For equivariantly formal actions, we also examine what cohomological information of the stratification is encoded. In the smooth setting we show that under certain conditions -- which in particular hold for a compact orientable manifold with discrete fixed point set -- the equivariant cohomologies of the strata are encoded in the equivariant cohomology of the manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_14038 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Reconstructing the orbit type stratification of a torus action from its equivariant cohomology Goertsches, Oliver Zoller, Leopold Algebraic Topology 57R91, 55N91 We investigate what information on the orbit type stratification of a torus action on a compact space is contained in its rational equivariant cohomology algebra. Regarding the (labelled) poset structure of the stratification we show that equivariant cohomology encodes the subposet of ramified elements. For equivariantly formal actions, we also examine what cohomological information of the stratification is encoded. In the smooth setting we show that under certain conditions -- which in particular hold for a compact orientable manifold with discrete fixed point set -- the equivariant cohomologies of the strata are encoded in the equivariant cohomology of the manifold. |
| title | Reconstructing the orbit type stratification of a torus action from its equivariant cohomology |
| topic | Algebraic Topology 57R91, 55N91 |
| url | https://arxiv.org/abs/2012.14038 |