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arXiv · 2407.07381

The de Rham cohomology of a Lie group modulo a dense subgroup

Brant Clark·Francois Ziegler
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Abstract

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 $\{Z\in\mathfrak g:\exp(tZ)\in H \text{ for all } t\in\mathbf R\}$.

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Brant Clark, Francois Ziegler. 2024-07-10. The de Rham cohomology of a Lie group modulo a dense subgroup. https://doi.org/10.1090/proc/17595

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