The space of relative orders and a generalization of Morris indicability theorem

Yago Antolín; Cristóbal Rivas

The space of relative orders and a generalization of Morris indicability theorem

Group Theory 2018-06-12 v2 Dynamical Systems

Authors: Yago Antolín , Cristóbal Rivas

Abstract

We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if $G$ is a finitely generated group acting by order preserving homeomorphism of on the line, then if some stabilizer of a point is proper and co-amenable subgroup, then $G$ surjects onto $\mathbb{Z}$ . This is a generalization of a theorem of Morris.

Keywords

relative orders finitely generated groups order preserving homeomorphisms co-amenable subgroups Morris indicability theorem

Cite

@article{arxiv.1802.05217,
  title  = {The space of relative orders and a generalization of Morris indicability theorem},
  author = {Yago Antolín and Cristóbal Rivas},
  journal= {arXiv preprint arXiv:1802.05217},
  year   = {2018}
}

Comments

v2: 10 pages, 2 figures. Typos corrected, Lemma 3.3 split into two statements affecting the numbering

The space of relative orders and a generalization of Morris indicability theorem

Abstract

Keywords

Cite

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