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

Abstract

We prove that the group ${\mathrm{QI}}^{+}(\mathbb{R})$ of orientation-preserving quasi-isometries of the real line is a left-orderable, non-simple group, which cannot act effectively on the real line $\mathbb{R}.$

arXiv commentMinor changes; final version, to appear in Algebraic and Geometric Topology