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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07381 |
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| _version_ | 1866918457929367552 |
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| author | Clark, Brant Ziegler, Francois |
| author_facet | Clark, Brant Ziegler, Francois |
| contents | Let $H$ be a dense subgroup of a Lie group $G$ with Lie algebra $\mathfrak g$. We show that the (diffeological) de Rham cohomology of $G/H$ equals the Lie algebra cohomology of $\mathfrak g/\mathfrak h$, where $\mathfrak h$ is the ideal $\{Z\in\mathfrak g:\exp(tZ)\in H \text{ for all } t\in\mathbf R\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The de Rham cohomology of a Lie group modulo a dense subgroup Clark, Brant Ziegler, Francois Differential Geometry Algebraic Topology 58A12, 57T15, 17B56, 58A40, 22E15 Let $H$ be a dense subgroup of a Lie group $G$ with Lie algebra $\mathfrak g$. We show that the (diffeological) de Rham cohomology of $G/H$ equals the Lie algebra cohomology of $\mathfrak g/\mathfrak h$, where $\mathfrak h$ is the ideal $\{Z\in\mathfrak g:\exp(tZ)\in H \text{ for all } t\in\mathbf R\}$. |
| title | The de Rham cohomology of a Lie group modulo a dense subgroup |
| topic | Differential Geometry Algebraic Topology 58A12, 57T15, 17B56, 58A40, 22E15 |
| url | https://arxiv.org/abs/2407.07381 |