Finitely presented simple left-orderable groups in the landscape of Richard Thompson's groups

Abstract

We construct the first examples of finitely presented simple groups of orientation-preserving homeomorphisms of the real line. Our examples are also of type $F_{\infty }$, have infinite geometric dimension, and admit a nontrivial homogeneous quasimorphism (and hence have infinite commutator width).

arXiv comment10 pages. The proofs have been streamlined. To appear in Annales Scientifiques de l'École Normale Supérieure