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$\R$-trees and laminations for free groups I: Algebraic laminations

Thierry Coulbois·Arnaud Hilion·Martin Lustig
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Abstract

This paper is the first of a sequence of three papers, where the concept of an $\mathbb R$-tree dual to a measured geodesic lamination in a hyperbolic surface is generalized to arbitrary $\mathbb R$-trees provided with a (very small) action of the free group $F_N$ of finite rank $N\geq 2$ by isometries. Three different definitions are given and they are proved to be equivalent. We also describe the topology and Out$(F_N)$-action on the space of laminations.

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Thierry Coulbois, Arnaud Hilion, Martin Lustig. 2007-06-09. $\R$-trees and laminations for free groups I: Algebraic laminations. https://doi.org/10.1112/jlms%2Fjdn052

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