New examples of groups acting on real trees

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 $\mathbb{R}$-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 (F$\mathbb{R}$).

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

References in corpus (3)

• Actions of finitely generated groups on R-trees
• On Residualizing Homomorphisms Preserving Quasiconvexity
• An (FA)-group that is not (FR)

Cited by in corpus (3)

• Roller boundaries for median spaces and algebras
• Superrigidity of actions on finite rank median spaces
• Wreath products of groups acting with bounded orbits