Ping-pong configurations and circular orders on free groups

Abstract : We discuss actions of free groups on the circle with “ping-pong” dynamics, i.e. dynamics determined by a finite amount of combinatorial data. As a natural extension of the work started in (Mann, Rivas, 2016), we show that the free group $F_n$ admits an isolated circular order if and only if n is even, in stark contrast with the case for linear orders. Following the work of Alvarez, Barrientos, Filimonov, Kleptsyn, Malicet, Meniño, and Triestino, we also exhibit examples of "exotic" isolated points in the space of all circular orders on $F_2$. As an application, we obtain analogous results for the linear orders on the groups $F_n\times \mathbb{Z}$.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01583550
Contributeur : Michele Triestino <>
Soumis le : jeudi 7 septembre 2017 - 15:15:08
Dernière modification le : vendredi 8 septembre 2017 - 15:42:01

Fichier

IsolatedCOv7.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01583550, version 1
  • ARXIV : 1709.02348

Collections

Citation

Dominique Malicet, Kathryn Mann, Cristóbal Rivas, Michele Triestino. Ping-pong configurations and circular orders on free groups. 2017. <hal-01583550>

Partager

Métriques

Consultations de
la notice

74

Téléchargements du document

9