Indecomposable $F_N$-trees and minimal laminations

Abstract

We extend the techniques of [8] 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 indecomposable if and only if its dual lamination is minimal up to diagonal leaves. Our main result generalizes [3, Proposition 1.8] as well as the main result of [22].