ℝ-trees, dual laminations and compact systems of partial isometries

Abstract

Abstract Let F N be a free group of finite rank N ≥ 2, and let T be an ℝ-tree with a very small, minimal action of F N with dense orbits. For any basis of F N there exists a heart $K_{\CAr}$ ⊂ (= the metric completion of T ) which is a compact subtree that has the property that the dynamical system of partial isometries a i : $K_{\CAr} \cap a_{i} K_{\CAr} \to a_{i}\inv K_{\CAr} \cap K_{\CAr}$ , for each a i ∈ , defines a tree $T_{(K_{\CAn}, \CAr)}$ which contains an isometric copy of T as minimal subtree.

Locations

• Mathematical Proceedings of the Cambridge Philosophical Society - View
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