Invariant laminations for irreducible automorphisms of free groups

Details Invariant laminations for irreducible automorphisms of free groups Invariant laminations for irreducible automorphisms of free groups

2011-04-07

arxiv.org/abs/1104.1265v2

Mathematics

Group Theory

Scientific paper

For every atoroidal iwip automorphism $\phi$ of $\FN$ (i.e. the analogue of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree $T_+(\phi)$ is obtained as "diagonal closure" of the support of the backward limit current $\mu_-(\phi)$. This diagonal closure is obtained through a finite procedure in analogy to adding diagonal leaves from the complementary components to the stable lamination of a pseudo-Anosov homeomorphism. We also give several new characterizations as well as a structure theorem for the dual lamination of $T_+(\phi)$, in terms of Bestvina-Feighn-Handel's "stable lamination" associated to $\phi$.

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