Topological transitivity and wandering intervals for group actions on the line

  • Enhui Shi

    Soochow University, Suzhou, China
  • Lizhen Zhou

    Soochow University, Suzhou, China
Topological transitivity and wandering intervals for group actions on the line $\mathbb R$ cover
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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