Avatars of Margulis invariants and proper actions
[Avatars des invariants de Margulis et actions propres]
Ghosh, Sourav1
1Ashoka University, Rajiv Gandhi Education City, Sonipat, Haryana 131029, India
Annales de l'Institut Fourier, Online first, 52 p.

In this article, we provide a necessary and sufficient criterion for proper actions on $\mathbb{H}^{n,n-1}$ in terms of certain special Anosov representations in $\mathsf {SO}(n,n)$. Moreover, we show that affine Anosov representations of any word hyperbolic group in $\mathsf {SO}(n,n-1)\ltimes \mathbb{R}^{2n-1}$ are infinitesimal versions of such special Anosov representations. Finally, using the above two results we interpret Margulis spacetimes as infinitesimal versions of quotient manifolds of $\mathbb{H}^{n,n-1}$.

In the appendix, we give a description of the appropriate cross-ratios in our setting and their infinitesimal versions.

Dans cet article, nous fournissons un critère nécessaire et suffisant pour des actions propres sur l’espace $\mathbb{H}^{n, n-1}$ en termes de certaines représentations Anosov spéciales dans le groupe $\mathsf {SO}(n,n)$. De plus, nous montrons que les représentations Anosov affines de tout groupe hyperbolique dans le groupe $\mathsf {SO}(n,n-1)\ltimes \mathbb{R}^{2n-1}$ sont des versions infinitésimales de ces représentations Anosov spéciales. Enfin, en utilisant les deux résultats ci-dessus, nous interprétons les espaces-temps de Margulis comme des versions infinitésimales de variétés quotientes de l’espace $\mathbb{H}^{n,n-1}$.

En annexe, nous donnons une description des birapports appropriés dans notre contexte et de leurs versions infinitésimales.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3748
Classification : 22E40, 37D20
Keywords: Anosov representations, Proper actions, Margulis spacetimes
Mots-clés : Représentation Anosov, Action propres, Espaces-temps de Margulis

Ghosh, Sourav  1

1 Ashoka University, Rajiv Gandhi Education City, Sonipat, Haryana 131029, India 
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Ghosh, Sourav. Avatars of Margulis invariants and proper actions. Annales de l'Institut Fourier, Online first, 52 p.

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