Growth of intersection numbers for free group automorphisms

Abstract

For a fully irreducible automorphism ϕof the free group F_k we compute the asymptotics of the intersection number n \mapsto i(T,T'ϕ^n) for trees T,T' in Outer space. We also obtain qualitative information about the geometry of the Guirardel core for the trees T and T'ϕ^n for n large.

33 pages, 6 figures, incorporates referee's suggestions

Cited by in corpus (5)

• Sphere paths in outer space
• Fully irreducible Automorphisms of the Free Group via Dehn twisting in ${♯}_k(S^2\times S^1)$
• Uniform independence for Dehn twist automorphisms of a free group
• Uniform fellow traveling between surgery paths in the sphere graph
• Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space