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

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.

arXiv commentto appear in the Illinois Journal of Math

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