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