Kapovich, Ilya; Lustig, Martin Invariant laminations for irreducible automorphisms of free groups. (English) Zbl 1348.20035 Q. J. Math. 65, No. 4, 1241-1275 (2014). 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 \(\varphi\). Cited in 1 ReviewCited in 7 Documents 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 Keywords:irreducible automorphisms; hyperbolic automorphisms; free groups; algebraic lamination; pseudo-Anosov homeomorphisms PDFBibTeX XMLCite \textit{I. Kapovich} and \textit{M. Lustig}, Q. J. Math. 65, No. 4, 1241--1275 (2014; Zbl 1348.20035) Full Text: DOI arXiv