an:06389448
Zbl 1348.20035
Kapovich, Ilya; Lustig, Martin
Invariant laminations for irreducible automorphisms of free groups
EN
Q. J. Math. 65, No. 4, 1241-1275 (2014).
00340459
2014
j
20E36 20E05 20F65 37D20 57M07
irreducible automorphisms; hyperbolic automorphisms; free groups; algebraic lamination; pseudo-Anosov homeomorphisms
Summary: For every irreducible hyperbolic automorphism \(\varphi\) of \(F_N\) (i.e. the analog of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree \(T_+(\varphi)\) is obtained as `diagonal closure' of the support of the backward limit current \(\mu_-(\varphi)\). This diagonal closure is obtained through a finite procedure analogous 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 \(T_+(\varphi)\), in terms of Bestvina-Feighn-Handel's `stable lamination' associated to \(\varphi\).