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Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2009

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

Résumé

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

hal-00198807 , version 1 (18-12-2007)
hal-00198807 , version 2 (22-10-2008)
hal-00198807 , version 3 (01-04-2009)

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Citer

Thierry Coulbois, Arnaud Hilion, Martin Lustig. $\R$-trees, dual laminations, and compact systems of partial isometries. Mathematical Proceedings of the Cambridge Philosophical Society, 2009, 147 (2), pp.345-368. ⟨10.1017/S0305004109002436⟩. ⟨hal-00198807v3⟩
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