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

By T. Coulbois, A. Hilion, Martin Lustig. 2007

49 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/723d9d02a1514f5d5f257f7fd61facfe5dd4108a

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dynamics on Berkovich Spaces in Low Dimensions (2012, unknown): “ace and usually considered with its metric topology. On the other hand, the notion of the weak topology on an R-tree seems to have been rediscovered several times, sometimes under dierent names (see [CLM07]). Our denitions of trees and metric trees are new but equivalent8 to the ones given in [FJ04]”
The boundary of the complex of free factors (2012, background): “nsider actions by homeomorphisms of FN on dendrites, which are compact, locally connected, uniquely arcwise connected metrizable spaces, see e.g. [Why63]. The connection to actions in ∂cvN comes from [CHL07]. The weak topology, also called the observers’ topology in [CHL07], on T has as subbasis the”