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arXiv · 0706.1313

Non-unique ergodicity, observers' topology and the dual algebraic lamination for $\R$-trees

Thierry Coulbois·Arnaud Hilion·Martin Lustig
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Abstract

We continue in this article the study of laminations dual to very small actions of a free group F on R-trees. We prove that this lamination determines completely the combinatorial structure of the R-tree (the so-called observers' topology). On the contrary the metric is not determined by the lamination, and an R-tree may be equipped with different metrics which have the same observers' topology.

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Thierry Coulbois, Arnaud Hilion, Martin Lustig. 2007-06-09. Non-unique ergodicity, observers' topology and the dual algebraic lamination for $\R$-trees. https://arxiv.org/abs/0706.1313

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