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$$\mathbb{R}$$-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.

##### MSC:
 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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