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arXiv · 0904.1533

Free group automorphisms with many fixed points at infinity

Andre Jaeger·Martin Lustig
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Abstract

A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as well as 2n repelling fixed points at bdry F_n. As a consequence of a recent result of V Guirardel there can not be more fixed points on bdry F_n, so that this family provides the answer to a question posed by G Levitt.

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Andre Jaeger, Martin Lustig. 2009-04-09. Free group automorphisms with many fixed points at infinity. https://doi.org/10.2140/gtm.2008.14.321

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