Indecomposable $F_N$-trees and minimal laminations

Thierry Coulbois (1) , Arnaud Hilion (1) , Patrick Reynolds (2)

1 I2M - Institut de Mathématiques de Marseille
2 MU - Miami University [Ohio]

We extend the techniques of [CH] to build an inductive procedure for studying actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty being an adaptation of the classical Rauzy-Veech induction for studying actions of surface type. As an application, we prove that a tree in the boundary of Outer space is free and indecomposableif and only if its dual lamination is minimal up to diagonal leaves. Our main result generalizes [BFH97, Proposition 1.8] as well as the main result of [KL11].

Domaines: Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Thierry Coulbois, Arnaud Hilion, Patrick Reynolds. Indecomposable $F_N$-trees and minimal laminations. Groups, Geometry, and Dynamics, 2015, 9 (2), pp.567-597. ⟨hal-01218334⟩