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

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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Submitted on : Saturday, June 9, 2007 - 1:23:05 PM
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Thierry Coulbois, Arnaud Hilion, Martin Lustig. $\R$-trees and laminations for free groups I: Algebraic laminations. Proceedings of the London Mathematical Society, London Mathematical Society, 2008, 78, pp.723-736. ⟨hal-00094735v2⟩

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