Ping-pong configurations and circular orders on free groups
Dominique Malicet
Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, FranceKathryn Mann
Cornell University, Ithaca, USACristóbal Rivas
Universidad de Santiago de Chile, ChileMichele Triestino
Université de Bourgogne Franche-Comté, Dijon, France
Abstract
We discuss actions of free groups on the circle with “ping-pong” dynamics; these are dynamics determined by a finite amount of combinatorial data, analogous to Schottky domains orMarkov partitions. Using this, we show that the free group admits an isolated circular order if and only if is even, in stark contrast with the case for linear orders. This answers a question from [21]. Inspired by work in [2], we also exhibit examples of “exotic” isolated points in the space of all circular orders on . Analogous results are obtained for linear orders on the groups .
Cite this article
Dominique Malicet, Kathryn Mann, Cristóbal Rivas, Michele Triestino, Ping-pong configurations and circular orders on free groups. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1195–1218
DOI 10.4171/GGD/519