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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 \(\varphi\).

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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