$\R$-trees and laminations for free groups III: Currents and dual $\R$-tree metrics

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

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

This is the third of a series of three articles where we introduce laminations for the free-groups. We explore here the link between currents and laminations and prove that the situation is more complicated than in the surface case of real tree dual to a measured geodesic lamination.

Mots clés: free groups; laminations; currents; uniquely ergodic; real trees; outer space; culler-vogtman

Domaines: Théorie des groupes [math.GR]

Thierry Coulbois, Arnaud Hilion, Martin Lustig. $\R$-trees and laminations for free groups III: Currents and dual $\R$-tree metrics. Proceedings of the London Mathematical Society, 2008, 78, pp.755-766. ⟨hal-00151896⟩