Finitely Presented Groups Acting on Trees

Abstract

It is shown that for any action of a finitely presented group $G$ on an $\mathbb{R}$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there is no global fixed point, then $G$ has a non-trivial action on a simplcial $\mathbb{R}$-tree.

18 pages, 8 figures. An incorrect example has been removed and the main result corrected

References in corpus (1)

• An (FA)-group that is not (FR)

Cited by in corpus (1)

• Proper decompositions of finitely presented groups