On Dense Subgroups of Homeo(I)

Azer Akhmedov

On Dense Subgroups of Homeo(I)

Group Theory 2026-04-14 v2 Dynamical Systems Geometric Topology

Authors: Azer Akhmedov

Abstract

We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of $\mathrm{Homeo}_{+}(I)$ admits a faithful discrete representation in it. In the last section, we demonstrate that finitely generated dense subgroups have infinite girth.

Keywords

Homeo_+(I) dense subgroup elementary amenable stability of generators finitely generated subgroup infinite girth

Cite

@article{arxiv.1312.1654,
  title  = {On Dense Subgroups of Homeo(I)},
  author = {Azer Akhmedov},
  journal= {arXiv preprint arXiv:1312.1654},
  year   = {2026}
}

Comments

This is the version that has existed in author's webpage since 2014 with a further modification/addition in the last section to extend the result (by a short argument) to all compact manifolds

On Dense Subgroups of Homeo(I)

Abstract

Keywords

Cite

Comments

Related papers