Exotic actions on trees. (English) Zbl 0872.20028

Holton, Charles; Zamboni, Luca Q.

Bull. Lond. Math. Soc. 29, No. 3, 309-313 (1997).

Summary: We give an explicit example of an exotic (non-simplicial), geometric free action of the free group \(\mathbb{F}_3\) on an \(\mathbb{R}\)-tree \(T\). We begin by associating an interval translation mapping of the unit interval to an automorphism \(\psi\) of \(\mathbb{F}_3\). We use a result of D. Gaboriau and G. Levitt to obtain an \(\mathbb{F}_3\)-action on an \(\mathbb{R}\)-tree \(T\). We show that for our particular choice of \(\psi\), the resulting \(\mathbb{F}_3\)-action is minimal, free and exotic.

MSC:

20E08	Groups acting on trees
20E36	Automorphisms of infinite groups
20E05	Free nonabelian groups

Keywords:

geometric free actions; free groups; interval translation mappings; automorphisms