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September 2019 A local rigidity theorem for finite actions on Lie groups and application to compact extensions of Rn
Ali Baklouti, Souhail Bejar, Ramzi Fendri
Kyoto J. Math. 59(3): 607-618 (September 2019). DOI: 10.1215/21562261-2019-0018

Abstract

Let G be a Lie group, and let Γ be a finite group. We show in this article that the space Hom(Γ,G)/G is discrete and—in addition—finite if G has finitely many connected components. This means that in the case in which Γ is a discontinuous group for the homogeneous space G/H, where H is a closed subgroup of G, all the elements of Kobayashi’s parameter space are locally rigid. Equivalently, any Clifford–Klein form of finite fundamental group does not admit nontrivial continuous deformations. As an application, we provide a criterion of local rigidity in the context of compact extensions of Rn.

Citation

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Ali Baklouti. Souhail Bejar. Ramzi Fendri. "A local rigidity theorem for finite actions on Lie groups and application to compact extensions of Rn." Kyoto J. Math. 59 (3) 607 - 618, September 2019. https://doi.org/10.1215/21562261-2019-0018

Information

Received: 7 February 2017; Revised: 12 April 2017; Accepted: 25 April 2017; Published: September 2019
First available in Project Euclid: 11 June 2019

zbMATH: 07108004
MathSciNet: MR3990179
Digital Object Identifier: 10.1215/21562261-2019-0018

Subjects:
Primary: 22E27
Secondary: 22E40 , 57S30

Keywords: discontinuous group , Euclidean motion group , Lie group , proper action , rigidity

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 3 • September 2019
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