Coulbois, Thierry; Hilion, Arnaud; Lustig, Martin \(\mathbb{R}\)-trees and laminations for free groups. I: Algebraic laminations. (English) Zbl 1197.20019 J. Lond. Math. Soc., II. Ser. 78, No. 3, 723-736 (2008). Summary: This paper is the first of a sequence of three papers, where the concept of a real tree dual to a measured geodesic lamination in a hyperbolic surface is generalized to arbitrary real trees provided with a (very small) action of a free group by isometries. Laminations for free groups are defined with care in three different approaches: algebraic laminations, symbolic laminations, and laminary languages. The topology on the space of laminations and the action of the outer automorphism group are detailed. Cited in 1 ReviewCited in 32 Documents MSC: 20E05 Free nonabelian groups 20E08 Groups acting on trees 20F65 Geometric group theory 37B10 Symbolic dynamics 57M07 Topological methods in group theory Keywords:real trees; actions of free groups by isometries; algebraic laminations; symbolic laminations; laminary languages; outer automorphism groups PDFBibTeX XMLCite \textit{T. Coulbois} et al., J. Lond. Math. Soc., II. Ser. 78, No. 3, 723--736 (2008; Zbl 1197.20019) Full Text: DOI arXiv