Coulbois, Thierry; Hilion, Arnaud; Reynolds, Patrick Indecomposable \(F_N\)-trees and minimal laminations. (English) Zbl 1342.20028 Groups Geom. Dyn. 9, No. 2, 567-597 (2015). 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)]. Cited in 1 ReviewCited in 6 Documents MSC: 20E08 Groups acting on trees 20E05 Free nonabelian groups 20F65 Geometric group theory 37A25 Ergodicity, mixing, rates of mixing 37B10 Symbolic dynamics Keywords:free groups; real trees; laminations; outer-space; Rauzy-Veech induction; indecomposable trees Citations:Zbl 1336.20033; Zbl 0884.57002; Zbl 1348.20035 PDFBibTeX XMLCite \textit{T. Coulbois} et al., Groups Geom. Dyn. 9, No. 2, 567--597 (2015; Zbl 1342.20028) Full Text: DOI arXiv References: [1] M. Bestvina and M. Feighn, Stable actions of groups on real trees. Invent. Math. 121 (1995), no. 2, 287-321. · Zbl 0837.20047 · doi:10.1007/BF01884300 [2] M. Bestvina and M. Feighn, Outer limits. Preprint 1994. [3] M. Bestvina, M. Feighn, and M. Handel, Laminations, trees, and irreducible au- tomorphisms of free groups. Geom. Funct. Anal. 7 (1997), no. 2, 215-244. · Zbl 0884.57002 · doi:10.1007/PL00001618 [4] M. Bestvina and M. Handel, Train tracks and automorphisms of free groups. Ann. of Math. (2) 135 (1992), no. 1, 1-51. · Zbl 0757.57004 · doi:10.2307/2946562 [5] A. J. Casson and S. A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston. London Mathematical Society Student Texts, 9. Cambridge University Press, Cambridge, 1988. · Zbl 0649.57008 [6] I. Chiswell, Introduction to \? -trees. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. · Zbl 1004.20014 [7] M. Cohen and M. Lustig, Very small group actions on R-trees and Dehn twist auto- morphisms. Topology 34 (1995), no. 3, 575-617. · Zbl 0844.20018 · doi:10.1016/0040-9383(94)00038-M [8] Th. Coulbois and A. Hilion, Rips induction: Index of the dual lamination of an R-tree. Groups Geom. Dyn. 8 (2014), no. 1, 97-134. · Zbl 1336.20033 [9] Th. Coulbois and A. Hilion, Ergodic currents dual to a real tree. Preprint 1013. [10] Th. Coulbois, A. Hilion, and M. Lustig, R-trees and laminations for free groups. I. Algebraic laminations. J. Lond. Math. Soc. (2) 78 (2008), no. 3, 723-736. · Zbl 1197.20019 · doi:10.1112/jlms/jdn052 [11] Th. Coulbois, A. Hilion, and M. Lustig, R-trees and laminations for free groups. II. the dual lamination of an R-tree. J. Lond. Math. Soc. (2) 78 (2008), no. 3, 737-754. · Zbl 1198.20023 · doi:10.1112/jlms/jdn053 [12] Th. Coulbois, A. Hilion, and M. Lustig, R-trees and laminations for free groups. III. Currents and dual R-tree metrics. J. Lond. Math. Soc. (2) 78 (2008), no. 3, 755-766. · Zbl 1200.20018 · doi:10.1112/jlms/jdn054 [13] Th. Coulbois, A. Hilion, and M. Lustig, R-trees, dual laminations and compact systems of partial isometries. Math. Proc. Cambridge Philos. Soc. , 147(2):345- 368, 2009. Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 2, 345-368. · Zbl 1239.20030 · doi:10.1017/S0305004109002436 [14] M. Culler and K. Vogtmann, Moduli of graphs and automorphisms of free groups. Invent. Math. 84 (1986), no. 1, 91-119. · Zbl 0589.20022 · doi:10.1007/BF01388734 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.