Indecomposable $$F_N$$-trees and minimal laminations.(English)Zbl 1342.20028

Summary: We extend the techniques of [T. Coulbois and A. Hilion, Groups Geom. Dyn. 8, No. 1, 97-134 (2014; Zbl 1336.20033)] 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 [M. Bestvina, M. Feighn, M. Handel, Geom. Funct. Anal. 7, No. 2, 215-244 (1997; Zbl 0884.57002), Proposition 1.8] as well as the main result of [I. Kapovich and M. Lustig, Q. J. Math. 65, No. 4, 1241-1275 (2014; Zbl 1348.20035)].

MSC:

 20E08 Groups acting on trees 20E05 Free nonabelian groups 20F65 Geometric group theory 37A25 Ergodicity, mixing, rates of mixing 37B10 Symbolic dynamics
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References:

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