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A non-residually finite group acting uniformly properly on a hyperbolic space
[Un exemple de groupe non résiduellement fini muni d’une action uniformément propre sur un espace hyperbolique]
Rémi Coulon1 ; Denis Osin2
1 Université de Rennes, CNRS, IRMAR - UMR 6625 Campus de Beaulieu, 263 avenue du Général Leclerc, F-35000 Rennes, France
2 Department of Mathematics, Vanderbilt University Nashville, TN 37240, U.S.A.
Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 19-30.

Dans cet article nous construisons un exemple de groupe qui n’est pas résiduellement fini et qui est muni d’une action uniformément propre sur un espace hyperbolique au sens de Gromov.

In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.86
Classification : 20F65, 20F67, 20E26, 20F06
Keywords: Hyperbolic spaces, residually finite group, small cancellation theory, uniformly proper action, bounded geometry
Mot clés : Espaces hyperboliques, groupes résiduellement finis, théorie de la petite simplification, action uniformément propre, géométrie bornée

Rémi Coulon 1 ; Denis Osin 2

1 Université de Rennes, CNRS, IRMAR - UMR 6625 Campus de Beaulieu, 263 avenue du Général Leclerc, F-35000 Rennes, France
2 Department of Mathematics, Vanderbilt University Nashville, TN 37240, U.S.A.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A non-residually finite group acting uniformly properly on a hyperbolic space},
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Rémi Coulon; Denis Osin. A non-residually finite group acting uniformly properly on a hyperbolic space. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 19-30. doi : 10.5802/jep.86. https://jep.centre-mersenne.org/articles/10.5802/jep.86/

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