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Invariant laminations for irreducible automorphisms of free groups. (English) Zbl 1348.20035
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 \(\varphi\).

MSC:
20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
20F65 Geometric group theory
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
57M07 Topological methods in group theory
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