A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910987741822976 |
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| author | Kaspersen, Eiolf Quick, Gereon |
| author_facet | Kaspersen, Eiolf Quick, Gereon |
| contents | We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their classifying spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups Kaspersen, Eiolf Quick, Gereon Algebraic Topology 57R77, 57T10, 55R35, 55S05, 55S10 We give a complete description of which non-torsion generators are not in the image of the Thom morphism from complex cobordism to integral cohomology for the classifying space of exceptional Lie groups except for E_8. We then show that the Thom morphism is not surjective for the classifying space of the gauge group of a principal E_7-bundle over the four-dimensional sphere. We use the results to detect nontrivial elements in the kernel of the reduced Thom morphism for Lie groups and their classifying spaces. |
| title | A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups |
| topic | Algebraic Topology 57R77, 57T10, 55R35, 55S05, 55S10 |
| url | https://arxiv.org/abs/2405.12717 |