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

Abstract

We construct examples of finitely generated groups L that have non-trivial actions on $\mathbb{R}$-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.

This paper has been withdrawn by the authors. The paper has been withdrawn as its arguments require further verification

References in corpus (1)

• A note on quotients of word hyperbolic groups with Property (T)

Cited by in corpus (3)

• New examples of groups acting on real trees
• Amenable groups without finitely presented amenable covers
• Finitely Presented Groups Acting on Trees