Ping-pong configurations and circular orders on free groups

  • Dominique Malicet

    Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France
  • Kathryn Mann

    Cornell University, Ithaca, USA
  • Cristóbal Rivas

    Universidad de Santiago de Chile, Chile
  • Michele Triestino

    Université de Bourgogne Franche-Comté, Dijon, France
Ping-pong configurations and circular orders on free groups cover
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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