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\(\mathbb{R}\)-trees and laminations for free groups. II: The dual lamination of an \(\mathbb{R}\)-tree. (English) Zbl 1198.20023

Summary: We define a dual lamination for any isometric very small \(F_N\)-action on an \(\mathbb{R}\)-tree \(T\). We obtain an \(\text{Out}(F_N)\)-equivariant map from the boundary of the outer space to the space of laminations. This map generalizes the corresponding basic construction for surfaces. It fails to be continuous. We then focus on the case where the tree \(T\) has dense orbits. In this case, we give two other equivalent constructions, but of different nature, of the dual lamination.
For part I cf. the authors, ibid. 78, No. 3, 723-736 (2008; Zbl 1197.20019).

MSC:

20E05 Free nonabelian groups
20E08 Groups acting on trees
20F65 Geometric group theory
37B10 Symbolic dynamics
57M07 Topological methods in group theory

Citations:

Zbl 1197.20019
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