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

Abstract

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.

Cited by in corpus (15)

• $\mathbb{R}$-trees and laminations for free groups II: The dual lamination of an $\mathbb{R}$-tree
• $\mathbb{R}$-trees and laminations for free groups I: Algebraic laminations
• Geometric Intersection Number and analogues of the Curve Complex for free groups
• The boundary of the complex of free factors
• Intersection form, laminations and currents on free groups
• Lines of minima in Outer space
• Algebraic laminations for free products and arational trees
• Ping-pong and Outer space
• North-South dynamics of hyperbolic free group automorphisms on the space of currents
• Stabilizers of $\mathbb{R}$-trees with free isometric actions of $F_N$
• Dynamics of hyperbolic iwips
• Subset currents on free groups
• Hyperbolic extensions of free groups from atoroidal ping-pong
• Ergodic currents dual to a real tree
• Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space