Van Est differentiation and integration
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914222169915392 |
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| author | Meinrenken, Eckhard Salazar, Maria Amelia |
| author_facet | Meinrenken, Eckhard Salazar, Maria Amelia |
| contents | The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, continuing an idea from [18], we revisit the van Est theory using the Perturbation Lemma from homological algebra. Using this technique, we obtain precise results for the van Est differentiation and integrations maps at the level of cochains. Specifically, we construct homotopy inverses to the van Est differentiation maps that are right inverses at the cochain level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_02080 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Van Est differentiation and integration Meinrenken, Eckhard Salazar, Maria Amelia Differential Geometry The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, continuing an idea from [18], we revisit the van Est theory using the Perturbation Lemma from homological algebra. Using this technique, we obtain precise results for the van Est differentiation and integrations maps at the level of cochains. Specifically, we construct homotopy inverses to the van Est differentiation maps that are right inverses at the cochain level. |
| title | Van Est differentiation and integration |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1906.02080 |