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

James Hyde; Yash Lodha

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

Group Theory 2023-12-27 v3

Authors: James Hyde , Yash Lodha

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).

Keywords

finitely presented groups simple groups left-orderable groups richard thompson groups homeomorphisms of the real line quasimorphism commutator width

Cite

@article{arxiv.2302.04805,
  title  = {Finitely presented simple left-orderable groups in the landscape of Richard Thompson's groups},
  author = {James Hyde and Yash Lodha},
  journal= {arXiv preprint arXiv:2302.04805},
  year   = {2023}
}

Comments

10 pages. The proofs have been streamlined. To appear in Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure

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

Abstract

Keywords

Cite

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