\(\mathbb{R}\)-trees and laminations for free groups. I: Algebraic laminations. (English) Zbl 1197.20019

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.


20E05 Free nonabelian groups
20E08 Groups acting on trees
20F65 Geometric group theory
37B10 Symbolic dynamics
57M07 Topological methods in group theory
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