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The group of quasi-isometries of the real line cannot act effectively on the line

Shengkui Ye and Yanxin Zhao

Algebraic & Geometric Topology 23 (2023) 3835–3847
Abstract

We prove that the group QI +() of orientation-preserving quasi-isometries of the real line is a left-orderable, nonsimple group, which cannot act effectively on the real line .

Keywords
quasi-isometric groups, left-orderable, real line
Mathematical Subject Classification
Primary: 20F65
References
Publication
Received: 26 March 2022
Revised: 28 May 2022
Accepted: 20 June 2022
Published: 5 November 2023
Authors
Shengkui Ye
NYU–ECNU Institute of Mathematical Sciences
NYU Shanghai
Shanghai
China
Yanxin Zhao
Department of Pure Mathematics
Xi’an Jiaotong–Liverpool University
Suzhou
Jiangsu
China

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