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

Abstract

In this report, we first recall the Poincaré's classification theorem for minimal orientation-preserving homeomorphisms on the circle and the Ghys' classification theorem for minimal orientation-preserving group actions on the circle. Then we introduce a classification theorem for a specified class of topologically transitive orientation-preserving group actions on the circle by ${\mathbb{Z}}^d$. Also, some groups that admit/admit no topologically transitive actions on the line are determined.

References in corpus (1)

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