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arXiv · 1710.02980

Topological transitivity and wandering intervals for group actions on the line $\mathbb R$

Enhui Shi·Lizhen Zhou
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Abstract

For every group $G$, we show that either $G$ has a topologically transitive action on the line $\mathbb R$ by orientation-preserving homeomorphisms, or every orientation-preserving action of $G$ on $\mathbb R$ has a wandering interval. According to this result, all groups are divided into two types: transitive type and wandering type, and the types of several groups are determined. We also show that every finitely generated orderable group of wandering type is indicable. As a corollary, we show that if a higher rank lattice $Γ$ is orderable, then $Γ$ is of transitive type.

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Enhui Shi, Lizhen Zhou. 2018-04-07. Topological transitivity and wandering intervals for group actions on the line $\mathbb R$. https://arxiv.org/abs/1710.02980

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