On locally trivial extensions of topological spaces by a pseudogroup

In this paper we restrict ourselves to the particular case where the pseudogroup is $\Gamma \ltimes G$ given by the action of a dense subgroup $\Gamma$ of a Lie group $G$ acting on $G$ by left translations. For a Riemannian foliation $F$ on a complete Riemannian manifold $M$ which is transversally p...

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Bibliographic Details
Main Authors Haefliger, Andre, Silva, Ana Maria Porto F
Format Journal Article
LanguageEnglish
Published 05.06.2017
Subjects
Mathematics - Algebraic Topology
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Summary:In this paper we restrict ourselves to the particular case where the pseudogroup is $\Gamma \ltimes G$ given by the action of a dense subgroup $\Gamma$ of a Lie group $G$ acting on $G$ by left translations. For a Riemannian foliation $F$ on a complete Riemannian manifold $M$ which is transversally parallelizable in the sense of Molino, let $X$ be the space of leaves closures. The holonomy pseudogroup of $F$ is an example of a locally trivial extension of $X$ by $\Gamma \ltimes G$. The study of a generalization of this particular case shall be the main purpose of this paper.
DOI:10.48550/arxiv.1706.01551