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Free group automorphisms with many fixed points at infinity
André Jäger and Martin Lustig
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Geometry & Topology Monographs 14
(2008) 321–333
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Abstract
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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.
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Keywords
free group, automorphism, fixed point at
infinity
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Mathematical Subject Classification
Primary: 20E36
Secondary: 57M05
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Publication
Received: 27 June 2006
Revised: 5 July 2007
Accepted: 31 July 2007
Published: 29 April 2008
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