Propriétés combinatoires du bord d’un groupe hyperbolique

Clais, Antoine

Séminaire de théorie spectrale et géométrie, Tome 32 (2014-2015), pp. 73-96.

Le but de ce survol est de présenter les modules combinatoires récemment utilisés pour étudier les propriétés quasi-conformes des bords des groupes hyperboliques. Dans un premier temps, on rappellera quelques résultats et questions de rigidité bien connus qui ont motivés l’introduction de ces outils. Puis on définira les modules combinatoires et la propriété de Loewner combinatoire qui offrent une nouvelle approche pour résoudre des problèmes ouverts depuis longtemps. Enfin, on décrira des applications concrètes de ces outils à travers quelques résultats récents et questions ouvertes.

Classification : 20F67, 30L10
Mots clés : Bord d’un groupe hyperbolique, analyse quasi-conforme, modules combinatoires

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