Approximating nonabelian free groups by groups of homeomorphisms of the real line

JOURNAL OF ALGEBRA

卷:563

Article

Lodha, Yash¹ 

[1] Ecole Polytech Fed Lausanne, Lausanne, Switzerland

关键词: Space of marked groups;    Left orderable;    Free group;    Piecewise;    Projective;    Torsion free;   

DOI  :  10.1016/j.jalgebra.2020.07.018

来源: Elsevier

【 摘 要 】

We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the space of marked groups is the free group of rank k with the standard marking. The class we consider consists of groups that admit actions satisfying mild dynamical conditions and a certain self-similarity type hypothesis. Examples include Thompson's group F, Higman-Thompson groups, Stein-Thompson groups, various Bieri-Strebel groups, the golden ratio Thompson group, and finitely presented nonamenable groups of piecewise projective homeomorphisms. For the case of Thompson's group F we provide a new and considerably simpler proof of this fact proved by Brin in [4]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free