English

New examples of groups acting on real trees

Group Theory 2017-05-17 v4

Abstract

We construct the first example of a finitely generated group which has Serre's property (FA) (i.e., whenever it acts on a simplicial tree it fixes a vertex), but admits a fixed point-free action on an R\mathbb{R}-tree with finite arc stabilizers. We also give a short and elementary construction of finitely generated groups that have property (FA) but do not have (FR\mathbb{R}).

Keywords

Cite

@article{arxiv.1403.1149,
  title  = {New examples of groups acting on real trees},
  author = {Ashot Minasyan},
  journal= {arXiv preprint arXiv:1403.1149},
  year   = {2017}
}

Comments

v4: 22 pages, revised following referee's suggestions. This version of the paper has been accepted by the Journal of Topology

R2 v1 2026-06-22T03:20:46.248Z