Volume 14 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

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