Topological transitivity and wandering intervals for group actions on the line
Enhui Shi
Soochow University, Suzhou, ChinaLizhen Zhou
Soochow University, Suzhou, China
![Topological transitivity and wandering intervals for group actions on the line $\mathbb R$ cover](/_next/image?url=https%3A%2F%2Fcontent.preview.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-13-issue-1.png&w=3840&q=90)
Abstract
For every group , we show that either has a topologically transitive action on the line by orientation-preserving homeomorphisms, or every orientation-preserving action of on 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 is orderable, then is of transitive type.
Cite this article
Enhui Shi, Lizhen Zhou, Topological transitivity and wandering intervals for group actions on the line . Groups Geom. Dyn. 13 (2019), no. 1, pp. 293–307
DOI 10.4171/GGD/485