Finitely generated infinite simple groups of homeomorphisms of the real line
Group Theory
2019-10-02 v2
Abstract
We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right) orderable groups. This answers a well known open question of Rhemtulla from 1980 concerning the existence of such groups. In fact, our construction provides a family of continuum many isomorphism types of groups with these properties.
Keywords
Cite
@article{arxiv.1807.06478,
title = {Finitely generated infinite simple groups of homeomorphisms of the real line},
author = {James Hyde and Yash Lodha},
journal= {arXiv preprint arXiv:1807.06478},
year = {2019}
}
Comments
21 pages. To appear in Inventiones Mathematicae