A local generalisation of frame bundles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866915486820728832 |
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| author | de Maujouy, Jérémie Pierard |
| author_facet | de Maujouy, Jérémie Pierard |
| contents | Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame bundles as a smooth manifold equipped with a coframe with value in a suitable Lie algebra and which furthermore satisfies a weakened version of the Maurer-Cartan equation. From this structure it is possible to construct a Lie algebra action on the manifold. We study the question of whether it is possible to construct a Lie group action and build a base manifold over which the initial manifold is a frame bundle. We find that generalised frame bundles can have singular underlying manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A local generalisation of frame bundles de Maujouy, Jérémie Pierard Differential Geometry 53C10 Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame bundles as a smooth manifold equipped with a coframe with value in a suitable Lie algebra and which furthermore satisfies a weakened version of the Maurer-Cartan equation. From this structure it is possible to construct a Lie algebra action on the manifold. We study the question of whether it is possible to construct a Lie group action and build a base manifold over which the initial manifold is a frame bundle. We find that generalised frame bundles can have singular underlying manifolds. |
| title | A local generalisation of frame bundles |
| topic | Differential Geometry 53C10 |
| url | https://arxiv.org/abs/2509.07749 |