An index for counting fixed points of automorphisms of free groups
D. Gaboriau, A. Jaeger, G.
Levitt, M. Lustig
Article publié :
Duke Math. J. 93 no. 3 (1998) 425-452.
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Abstract
Let a be an automorphism of a free group F of
rank n. The Scott conjecture, proved by Bestvina-Handel, states that the
fixed subgroup Fixa= {w Œ
Fn
| a (w) = w} has rank at most n. Using R-trees,
we show the stronger inequality
rkFix a+1/2
a (a)
£ n,
where a(a) is the number of Fix a-orbits
of attracting fixed points for the action of a
on the boundary of F.