an:05378283
Zbl 1198.20023
Coulbois, Thierry; Hilion, Arnaud; Lustig, Martin
\(\mathbb{R}\)-trees and laminations for free groups. II: The dual lamination of an \(\mathbb{R}\)-tree
EN
J. Lond. Math. Soc., II. Ser. 78, No. 3, 737-754 (2008).
00234922
2008
j
20E05 20E08 20F65 37B10 57M07
real trees; actions of free groups by isometries; algebraic laminations; symbolic laminations; laminary languages; outer space; outer automorphism groups
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).
Zbl 1197.20019