An (FA)-group that is not (FR)

2012/03/15 by Dunwoody, Martin J., Minasyan, Ashot
#20E08 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1203.3317

Abstract

We construct examples of finitely generated groups L that have non-trivial actions on ℝ-trees but which cannot act, without fixing a vertex, on any simplicial tree. Moreover, any finitely presented group mapping onto L does have a fixed point-free action on some simplicial tree.

Related

• Finitely Presented Groups Acting on Trees
• Groups acting faithfully on trees and properly on products of trees
• Actions of finitely generated groups on R-trees
• Non-nesting actions of groups on real trees vs isometric actions
• Simple groups of automorphisms of trees determined by their actions on finite subtrees