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ISSN (electronic): 1464-8997
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Free group automorphisms with many fixed points at infinity

André Jäger and Martin Lustig

Geometry & Topology Monographs 14 (2008) 321–333

DOI: 10.2140/gtm.2008.14.321

arXiv: 0904.1533

Abstract

A concrete family of automorphisms αn of the free group Fn is exhibited, for any n ≥ 3, and the following properties are proved: αn is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as well as 2n repelling fixed points at ∂Fn. As a consequence of a recent result of V Guirardel there can not be more fixed points on ∂Fn, so that this family provides the answer to a question posed by G Levitt.

Keywords

free group, automorphism, fixed point at infinity

Mathematical Subject Classification

Primary: 20E36

Secondary: 57M05

References
Publication

Received: 27 June 2006
Revised: 5 July 2007
Accepted: 31 July 2007
Published: 29 April 2008

Authors
André Jäger
Louis Pasteur-Strasse 58
60439 Frankfurt am Main
Germany
Martin Lustig
Mathématiques (LATP)
Université P Cézanne – Aix Marseille III
Ave E Normandie-Niemen
13397 Marseille 20
France