Topological conjugation classes of tightly transitive subgroups of ${\text{Homeo}}_{+}({\mathbb{S}}^1)$

Abstract

Let ${\text{Homeo}}_{+}({\mathbb{S}}^1)$ denote the group of orientation preserving homeomorphisms of the circle ${\mathbb{S}}^1$. A subgroup $G$ of ${\text{Homeo}}_{+}({\mathbb{S}}^1)$ is tightly transitive if it is topologically transitive and no subgroup $H$ of $G$ with $[G:H]=\infty$ has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of ${\text{Homeo}}_{+}({\mathbb{S}}^1)$ which are isomorphic to ${\mathbb{Z}}^n$ for any integer $n\ge 2$.

arXiv comment23 pages, 4 figures

Cited by in corpus (1)

• The realization and classification of topologically transitive group actions on $1$-manifolds