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

Thierry Coulbois (1) , Arnaud Hilion (1) , Martin Lustig (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Out$(F_N)$; laminations; $\mathbb R$-trees; Outer Space

Domaines: Théorie des groupes [math.GR]

Thierry Coulbois, Arnaud Hilion, Martin Lustig. $\R$-trees and laminations for free groups I: Algebraic laminations. Proceedings of the London Mathematical Society, 2008, 78, pp.723-736. ⟨hal-00094735v2⟩