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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
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