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Exotic actions on trees. (English) Zbl 0872.20028
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:
 2e+09 Groups acting on trees 2e+37 Automorphisms of infinite groups 2e+06 Free nonabelian groups
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