Group bundles and group connections
| Autor: | Blázquez-Sanz, David, Marín-Arango, Carlos A., Gordon, Sedney Suárez |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider smooth families of Lie groups (group bundles) and connections that are compatible with the group operation. We characterize the space of group connections on a group bundle as an affine space modeled over the vector space of $1$-forms with values cocycles in the Lie algebra bundle of the aforementioned group bundle. We show that group connections satisfy the Ambrose-Singer theorem and that group bundles can be seen as a particular case of associated bundles realizing group connections as associated connections. We give a construction of the Moduli space of group connections with fixed base and fiber, as an space of representations of the fundamental group of the base. Comment: 25 pages |
| Databáze: | arXiv |
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