English

On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$

Group Theory 2020-07-23 v2 Dynamical Systems

Abstract

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of Homeo(D,D)\mathrm{Homeo}(D,\partial D), the group of homeomorphisms of the disk fixing the boundary. This implies that the group Homeo(D,D)\mathrm{Homeo}(D,\partial D) itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.

Keywords

Cite

@article{arxiv.1912.05386,
  title  = {On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$},
  author = {Michele Triestino},
  journal= {arXiv preprint arXiv:1912.05386},
  year   = {2020}
}

Comments

7 pages, 1 figure; final version to appear in L'Enseignement Math\'ematique (2)