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arXiv · 1110.3506

Indecomposable $F_N$-trees and minimal laminations

Thierry Coulbois·Arnaud Hilion·Patrick Reynolds
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Abstract

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 he 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 [BFH97, Proposition 1.8] as well as the main result of [KL11].

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Thierry Coulbois, Arnaud Hilion, Patrick Reynolds. 2011-10-16. Indecomposable $F_N$-trees and minimal laminations. https://arxiv.org/abs/1110.3506

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