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Main Authors: Clark, Brant, Ziegler, Francois
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.07381
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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