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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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